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DOE OSTI2025

Crystal fields, exchange and dipolar interactions, and noncollinear magnons of erbium oxide

Here, we simulate the properties of magnons in erbium oxide, a noncollinear antiferromagnet, from an effective single-ion Hamiltonian, including exchange and long-range dipolar interactions. We parametrize the crystal-field splitting of Er 2 ⁢O 3 using Steven's operators and obtain the effective symmetry-dependent exchange constants between different erbium ions quenched by the crystal field at different symmetry sites. We apply the Holstein-Primakoff transformation to the noncollinear spin system and employ paraunitary diagonalization for the effective spin Hamiltonian. The addition of the dipolar interaction to the exchange magnon dispersion changes the magnon bands drastically. The long-range nature of the dipolar interaction provides challenges to convergence, however, we find that the averaged and normalized difference in the magnon dispersion is less than an averaged factor of 10 −6 if the dipolar interaction is included out to the 40th nearest neighbor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Quantum eigenvalue estimation via time series analysis

We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ε, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ε.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Neutrino flavor instabilities in neutron star mergers with moment transport: Slow, fast, and collisional modes

Determining where, when, and how neutrino flavor oscillations must be included in large-scale simulations of hot and dense astrophysical environments is an enduring challenge that must be tackled to obtain accurate predictions. Here, using an angular moment-based linear stability analysis framework, we examine the different kinds of flavor instabilities that can take place in the context of the postprocessing of a neutron star merger simulation, with a particular focus on the collisional flavor instability and a careful assessment of several commonly used approximations. First, neglecting anisotropies of the neutrino field, we investigate the extent to which commonly used monoenergetic growth rates reproduce the results obtained from a full multienergy treatment. Contrary to the large discrepancies found in core-collapse supernova environments, we propose a simple combination of energy-averaged estimates that reproduces the multienergy growth rates in our representative simulation snapshot. We then quantify the impact of additional physical effects, including nuclear many-body corrections, scattering opacities, and the inclusion of the vacuum term in the neutrino Hamiltonian. Finally, we include the neutrino distribution anisotropies, which allows us to explore, for the first time in a multienergy setting, the interplay between collisional, fast, and slow modes in a moment-based neutron star merger simulation. We find that, despite a dominance of the fast instability in most of the simulation volume, certain regions exhibit only a collisional instability, while others, especially at large distances, exhibit a slow instability that is largely underestimated if anisotropic effects are neglected.

neutrino oscillations↗
DOE OSTI2022

Quantum-Accurate Multiscale Modeling of Shock Hugoniots, Ramp Compression Paths, Structural and Magnetic Phase Transitions, and Transport Properties in Highly Compressed Metals

Fully characterizing high energy density (HED) phenomena using pulsed power facilities (Z machine) and coherent light sources is possible only with complementary numerical modeling for design, diagnostic development, and data interpretation. The exercise of creating numerical tests, that match experimental conditions, builds critical insight that is crucial for the development of a strong fundamental understanding of the physics behind HED phenomena and for the design of next generation pulsed power facilities. The persistence of electron correlation in HED materials arising from Coulomb interactions and the Pauli exclusion principle is one of the greatest challenges for accurate numerical modeling and has hitherto impeded our ability to model HED phenomena across multiple length and time scales at sufficient accuracy. An exemplar is a ferromagnetic material like iron, while familiar and widely used, we lack a simulation capability to characterize the interplay of structure and magnetic effects that govern material strength, kinetics of phase transitions and other transport properties. Herein we construct and demonstrate the Molecular-Spin Dynamics (MSD) simulation capability for iron from ambient to earth core conditions, all software advances are open source and presently available for broad usage. These methods are multi-scale in nature, direct comparisons between high fidelity density functional theory (DFT) and linear-scaling MSD simulations is done throughout this work, with advancements made to MSD allowing for electronic structure changes being reflected in classical dynamics. Main takeaways for the project include insight into the role of magnetic spins on mechanical properties and thermal conductivity, development of accurate interatomic potentials paired with spin Hamiltonians, and characterization of the high pressure melt boundary that is of critical importance to planetary modeling efforts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by [Huggins et al ., Nature (London) 603 , 416 (2022)] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling postprocessing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [Commun. Math. Phys. 404 , 629 (2023)], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical postprocessing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.

Monte Carlo methods↗
DOE OSTI2021

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. In conclusion, this advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

ORNL_AISD-Ex: Quantum chemical prediction of UV/Vis absorption spectra for over 10 million organic molecules

We performed calculations of electronic excitation energies and associated oscillator strengths based on the time-dependent density-functional tight-binding (TD-DFTB) method [1]. The SMILES (Simplified molecular-input line-entry system) strings of the molecules from the AISD HOMO-LUMO database [2] were converted to a 3D atomistic structure and stored in a PDB file after preliminary geometry optimization using the Merck Molecular Force Field (MMFF94) in RDKit [3,4]. The primary information stored in the PDB file archive consists of Cartesian coordinates for each atom of the molecule in their 3D location in space, along with summary information about the structure, sequence, and experiment. We then performed molecular geometry optimization using the density-functional tight-binding (DFTB) method [5] in the electronic ground state, followed by single-point excited states calculations, as described below. We note that, since RDKit employs a random choice for the generation of molecular conformers, the molecular geometries obtained in this dataset could be different from the ones that were generated when the AISD HOMO-LUMO dataset was generated. The computed excitation energies and associated oscillator strengths can be converted to predict UV/Vis absorption spectra, where excitation energies correspond to absorption peak positions, and oscillator strengths are a good measure of the probability of absorption of visible or UV light in transitions between electronic ground and excited states. The conversion of SMILES strings to 3D Cartesian coordinates of fully DFTB-optimized molecules was successful for 10,502,904 out of 10,502,917 molecules. For these molecules, both geometry optimizations and excited states calculations were successful. The DFTB calculations did not complete for 13 molecules of the original AISD HOMO-LUMO dataset. We still provide information about the geometry of these molecules. The molecules are diverse for chemical compositions (which span 5 non-hydrogen elements: oxygen, carbon, nitrogen, fluorine, sulfur) and molecular size (the smallest molecule contains 5 non-hydrogen atoms, and the largest molecule contains 71 non-hydrogen atoms). The DFTB method [5] is an approximation to density functional theory (DFT), utilizing a minimal basis set in conjunction with a two-center approximation to the electronic Hamiltonian and overlap matrix elements. The DFTB total energy is the sum of an electronic and a repulsive energy contribution, and their calculation requires optimized electronic parameters and diatomic repulsive potential energy functions. All DFTB calculations were performed using the DFTB+ code [6] (version 21.2) and the wrapper for DFTB+ in the Atomic Simulation Environment (ASE) (version 3.22.1) [7], which performed an internal conversion of Cartesian coordinates from PDB to the .gen file format. For the geometry optimizations on the electronic ground state potential energy surface of the molecules, we have chosen the third-order DFTB (DFTB3) method [5c] and employed the matching 3ob set of electronic parameters and repulsive potentials [8]. The empirical γ-damping for hydrogen bond correction, and Grimme's D3 empirical dispersion correction with Becke-Johnson damping (D3(BJ)) [9] dispersion correction was included to improve the description of non-covalent interactions. For excited states single-point energy calculations, we employed the TD-DFTB method in conjunction with the DFTB2 method [5b] and the matching mio [5b,10] and halorg [11] parameter sets. We opted to request the simultaneous calculation of 50 excited states for singlet transition to investigate sufficient number of excited states, based on linear response theory using the Casida equation [Ref: T. A. Niehaus, S. Suhai, F. Della Sala, P Lugli, M. Elstner, G. Seifert, and Th. Frauenheim. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 63:085108, 2001] and the ARPACK diagonalizer [R. B. Lehoucq, D. C. Sorensen, and C. Yang. Arpack users guide: Solution of large-scale eigenvalue problems by implicitly restarted arnoldi methods, 1997. 46, 51]. The dataset contains 1001 tar.gz files. Tar files are named as “ornl_aisd_ex_1.tar.gz†through “ornl_aisd_ex_1000.tar.gzâ€. Additionally, the 13 failed molecules are in “ornl_aisd_ex_unprocessed.tar.gzâ€. Except for the tar files listed below, each tar file contains 10,500 molecules. Tar files numbered 34, 121, 128, 352, 360, 429, 495, 509, 518, 627, 676, 668, and 862 contain 10,499 molecules each. The last tar file numbered 1000 contains 13,417 molecules. The total size of the uncompressed dataset is over 283 Gigabytes. The code for calculating the electronic excitation energies and statistical analysis of the dataset is provided at the following GitLab repository: https://github.com/ORNL/Analysis-of-Large-Scale-Molecular-Datasets-with-Python Calculating the UV spectrum of a molecule requires performing 3 main operations: 1. Converting the smiles string representation of a molecule into a geometric structure where each atom is assigned XYZ coordinates. The geometric structure is written to the file smiles.pdb. 2. Using smiles.pdb to compute the relaxed geometry of the molecule, which corresponds with the position of the atoms at the position of equilibrium at the ground state. This generates the files band.out, detailed.out, and geo_end.gen. 3. Using geo_end.gen to calculate the UV spectrum of the molecule which is written into the file EXC.DAT. Every molecule in the dataset has its own directory. The files contained in each molecule directory are as follows: 1. geo_end.gen 2. detailed.out 3. band.out 4. EXC.DAT 5. smiles.pdb REFERENCES [1] Niehaus, T. A.; Suhai, S.; Della Salla, F.; Lugli, P.; Elstner, M.; Seifert, G.; Frauenheim, Th. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 2001, 63, 085108/1-9. [2] Blanchard, A.; Gounley, J.; Metha, K.; Yoo, P.; Irle, S. AISD HOMO-LUMO. DOI: 10.13139/ORNLNCCS/1869409 [3] RDKit: Cheminformatics and Machine Learning Software. 2013, [http://www.rdkit.org] [4] Tosco, P.; Stiefl, N. and Landrum, G. Bringing the MMFF force field to the RDKit: implementation and validation. J Cheminform. 2014, 6, 1–4. [5] a) Porezag, D.; Frauenheim, T.; Kohler, T.; Seifert, G.; Kaschner, Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon, R. Phys. Rev. B 1995, 51, 12947-12957; b) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G.; Phys. Rev. B 1998, 58, 7260-7268; c) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB), J. Chem. Theory Comput. 2011, 7, 931-948; d) Cui, Q.; Elstner, M. Density functional tight binding: values of semi-empirical methods in an ab initio era, Phys. Chem. Chem. Phys. 2014, 16, 14368-14377. [6] Hourahine, B. et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations, J. Chem. Phys. 2020, 152, 124101/1-19. [7] Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys.: Cond. Matter 2017, 29, 273002. [8] Kubillus, M.; Kubar, T.; Gaus, M.; Rezac, J.; Elstner, M. Parameterization of the DFTB3 Method for Br, Ca, Cl, F, I, K, and Na in Organic and Biological Systems, J. Chem. Theory Comput. 2015, 11, 332-342. [9] Brandenburg, J. G.; Grimme, S. Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB), J. Phys. Chem. Lett. 2014, 5, 1785−1789. [10] a) Niehaus, T. A.; Elstner, M.; Frauenheim, Th.; Suhai, S. Application of an approximate density-functional method to sulfur containing compounds. J. Mol. Struct.: THEOCHEM 2001, 541, 185-94; b) Elstner, M.; Hobza, P.; Frauenheim, Th.; Suhai, S.; Kaxiras, E. Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment. J. Chem. Phys. 2001, 114, 5149-55. [11] Kubar, T.; Bodrog, Z.; Gaus, M.; Köhler, C.; Aradi, B.; Frauenheim, Th.; Elstner, M. Parametrization of the SCC-DFTB Method for Halogens. J. Chem. Theory Comput. 2013, 9, 2939-49.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Field Programmable Gate Arrays for Enhancing the Speed and Energy Efficiency of Quantum Dynamics Simulations

We present the first application of field programmable gate arrays (FPGAs) as new, customizable hardware architectures for carrying out fast and energy-efficient quantum dynamics simulations of large chemical/material systems. Instead of tailoring the software to fixed hardware, which is the typical case for writing quantum chemistry code for central processing units (CPUs) and graphics processing units (GPUs), FPGAs allow us to directly customize the underlying hardware (even at the level of specific electrical signals in the circuit) to give a truly optimized computational performance for quantum dynamics calculations. By offloading the most intensive and repetitive calculations onto an FPGA, we show that the computational performance of our real-time electron dynamics calculations can even exceed that of optimized commercial mathematical libraries running on high-performance GPUs. In addition to this impressive computational speedup, we show that FPGAs are immensely energy-efficient and consume 4 times less energy than modern GPU or CPU architectures. These energy savings are a practical and important metric for supercomputing centers (many of which exceed over $1 million in power costs alone), as exascale computing capabilities become more widespread and commonplace. Taken together, the implementation techniques and performance metrics of our study demonstrate that FPGAs could play a promising role in upcoming quantum chemistry and materials science applications, particularly for the acceleration and energy-efficient execution of quantum dynamics calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Efficient sparse state preparation via quantum walks

Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work, we develop an algorithm that converts single-edge and self-loop dynamic CTQWs to the gate model of computation. We use this mapping to introduce an efficient sparse quantum state preparation framework based on dynamic CTQWs. Our approach utilizes combinatorics techniques such as minimal hitting sets, minimum spanning trees, and shortest Hamiltonian paths to reduce the number of controlled gates required to prepare sparse states. We show that our framework encompasses the current state of the art ancilla-free sparse state preparation method by reformulating this method as a CTQW. This CTQW-based framework offers an alternative to the uniformly controlled rotation method used by Qiskit by requiring fewer CX gates when the target state has a polynomial number of non-zero amplitudes.

dynamic continuous time quantum walks↗
DOE OSTI2022

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

Here we study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green’s functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in D > 1 dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest 𝜂′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous 𝜂′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted 𝜂′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the 𝜂′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions.

Lattice field theory↗
DOE OSTI2026

Ab Initio Polariton Spectra of ZnTPP Molecules Collectively Coupled Inside an Optical Cavity

Exciton-polaritons are quasi-particles formed by the quantum mechanical hybridization of electronic and photonic excitations. Despite extensive investigations, a fundamental understanding of molecular polariton spectra and the polariton delocalization from an ab initio theoretical perspective remains elusive. We simulate experimentally measured linear transmission spectroscopy of many Zinc(II) tetraphenylporphyrin (ZnTPP) molecules collectively coupled to a cavity from first principles. Our theoretical approach incorporates many low-lying electronic excitations in ZnTPP molecules, as well as collective light-matter couplings between ZnTPP and the quantized radiation modes, both of which are shown to be the key to accurately recovering the experimental spectra. We further analyzed to what extent the polariton and dark states are delocalized over many molecules, for the first time, using fully ab initio descriptions of the molecules. We finally investigate the line width as a function of detuning, providing new theoretical insights into the experimentally observed motional narrowing behavior. Our work presents first-ofits- kind theoretical studies on molecular polariton spectra, offering a new perspective on molecular polariton formation in realistic ab initio molecular systems whose rich, many-state nature provides spectral features enabled by the high density of electronic states beyond simple quantum optics models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Furthermore, our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Vibronic exciton model for low bandgap donor–acceptor polymers

In this study, a vibronic exciton model is introduced to describe the excited state band structure and associated absorption spectra of low bandgap donor–acceptor conjugated polymers. The Hamiltonian is represented in a diabatic basis consisting of Frenkel-like donor and acceptor fragment excitations as well as charge-transfer (CT) excitations between neighboring fragments. States are coupled to each other through electron and hole transfer as well as Coulombically, through interacting fragment transition dipole moments. Local vibronic coupling involving the prominent aromatic-quinoidal vibrational mode, which is responsible for pronounced vibronic progressions in most conjugated oligomers and polymers, is also included. The DAD repeat unit is shown to behave like a J-aggregate trimer, driven by both the sizable in-phase electron and hole transfer integrals between donor and acceptor fragments as well as negative Coulomb coupling between donor and acceptor fragment excitations. The J-aggregate behavior is enhanced in the polymer limit through inter-repeat unit coupling, with the 0–0 vibronic peak significantly enhanced in the lowest-energy near-IR band. In addition, the radiative rate is enhanced by the number of coherently connected repeat units. The near-IR band is shown to possess roughly equal admixtures of CT and Frenkel-like excitations. Applications are made to the polymer PffBT4T-2DT, with the simulated absorption spectrum quantitatively capturing the salient features of the measured spectrum.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Symmetry breaking as predicted by a phase space Hamiltonian with a spin Coriolis potential

Here, we perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ( 3 CH 2 , 2 CH$^{•}_{3}$, 3 O 2 ) going beyond the Born–Oppenheimer approximation and accounting for nuclear motion. According to a phase space approach that parameterizes electronic states (|Φ⟩) and electronic energies (E) by nuclear position and momentum [i.e., |Φ(R, P)⟩ and E(R, P)], we find that the presence of degenerate spin degrees of freedom leads to broken symmetry ground states. More precisely, rather than a single degenerate minimum at (R, P) = (R min , 0), the ground state energy has two minima at (R,P)=(R' min ,±P min ) (where R' min is close to R min ), dramatically contradicting the notion that the total energy of the system can be written in separable form as E = $\frac{P^2}{2M}$ + V el . Although we find that the broken symmetry solutions have small barriers between them for the small molecules, we hypothesize that the barriers should be macroscopically large for metallic solids, thus offering up a new phase-space potential energy surface for simulating the Einstein–de Haas effect.

Berry connection↗
DOE OSTI2020

Classical discrete time crystals

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. To conclude, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Adaptive variational quantum eigensolvers for highly excited states

Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore the potential of variational quantum algorithms to approximate such states. We propose an adaptive variational quantum eigensolver (VQE) for excited states (X) that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian H by attempting to minimize the energy variance with respect to H. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable regimes, where we calculate various quantities of interest, including the total energy, magnetization density, and entanglement entropy. We also compare the performance of adaptive VQE-X to an adaptive variant of the folded-spectrum method. For both methods, we find a strong dependence of the algorithm's performance on the choice of operator pool used for the adaptive construction of the ansatz. In particular, an operator pool including long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. Here, we also study the scaling of the number of variational parameters with system size, finding that an exponentially large number of parameters may be necessary to approximate individual highly excited states. Nevertheless, we argue that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties of many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Universal thermodynamics of an SU ( N ) Fermi-Hubbard model

The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit U/t $\gg$ 1, it is effectively described by the Heisenberg Hamiltonian. In this limit, enlarging the spin and extending the typical SU(2) symmetry to SU(N) has been predicted to give exotic phases of matter in the ground state, with a complicated dependence on N. This raises the question of what—if any—are the finite-temperature signatures of these phases, especially in the currently experimentally relevant regime near or above the superexchange energy. We explore this question for thermodynamic observables by numerically calculating the thermodynamics of the SU(N) FHM in the two-dimensional square lattice near densities of one particle per site, using determinant quantum Monte Carlo and numerical linked cluster expansion. Interestingly, we find that for temperatures above the superexchange energy, where the correlation length is short, the energy, number of on-site pairs, and kinetic energy are universal functions of N. Although the physics in the regime studied is well beyond what can be captured by low-order high-temperature series, we show that an analytic description of the scaling is possible in terms of only one- and two-site calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗