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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2023

Time-Resolved Hanbury Brown–Twiss Interferometry of On-Chip Biphoton Frequency Combs Using Vernier Phase Modulation

Biphoton frequency combs (BFCs) are promising quantum sources for large-scale and high-dimensional quantum information and networking systems. In this context, the spectral purity of individual frequency bins will be critical for realizing quantum networking protocols like teleportation and entanglement swapping. Measurement of the temporal autocorrelation function of the unheralded signal or idler photons comprising the BFC is a key tool for characterizing their spectral purity and in turn verifying the utility of the biphoton state for networking protocols. Yet the experimentally obtainable precision for measuring BFC correlation functions is often severely limited by detector jitter. The fine temporal features in the correlation function—not only of practical value in quantum information, but also of fundamental interest in the study of quantum optics—are lost as a result. We propose a scheme to circumvent this challenge through electro-optic phase modulation, experimentally demonstrating time-resolved Hanbury Brown–Twiss characterization of BFCs generated from an integrated 40.5-GHz Si 3 N 4 microring, up to a 3×3-dimensional two-qutrit Hilbert space. Through slight detuning of the electro-optic drive frequency from the comb’s free spectral range, our approach leverages Vernier principles to magnify temporal features, which would otherwise be averaged out by detector jitter. We demonstrate our approach under both continuous-wave and pulsed-pumping regimes, finding excellent agreement with theory. In conclusion, our method reveals not only the collective statistics of the contributing frequency bins but also their temporal shapes—features lost in standard fully integrated autocorrelation measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Charge-density-wave melting in the one-dimensional Holstein model

We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the real-time evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photoinduced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state density-matrix renormalization group method for electron-phonon systems using local basis optimization. In our examples, we account for up to M ph =40 bare phonons per site by working with O(10) optimal phonon modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Absence of Fibonacci anyons in Rydberg chains

Recent experiments have focused attention on the properties of chains of atoms in which the atoms are either in their ground states or in highly excited Rydberg states which block similar excitations in their immediate neighbors. As the low-energy Hilbert space of such chains is isomorphic to that of a chain of Fibonacci anyons, they have been proposed as a platform for topological quantum computation and for simulating anyon dynamics. In this work, we show that generic local operators in the Rydberg chain correspond to nonlocal anyonic operators that do not preserve a topological symmetry of the physical anyons. Consequently, we argue that Rydberg chains do not yield Fibonacci anyons and quantum computation with Rydberg atoms is not topologically protected.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Theory of the phase transition in random unitary circuits with measurements

Here, we present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a nonanalytic change in the amount of information extracted by the measurements about the initial state of the system, quantified by the Fisher information. To compute the von Neumann entanglement entropy $\textit{S}$ and the Fisher information $\mathcal{F}$, we apply a replica method based on a sequence of quantities $\tilde{S}^{(n)}$ and $\mathcal{F}^{(n)}$ that depend on the $\textit{n}$th moments of density matrices and reduce to $\textit{S}$ and $\mathcal{F}$ in the limit $\textit{n}$ → 1. These quantities with $\textit{n}$ ≥ 2 are mapped to free energies of a classical spin model with $\textit{n}$! internal states in two dimensions with specific boundary conditions. In particular, $\tilde{S}^{(n)}$ is the excess free energy of a domain wall terminating on the top boundary, and $\mathcal{F}^{(n)}$ is related to the magnetization on the bottom boundary. Phase transitions occur as the spin models undergo ordering transitions in the bulk. Taking the limit of large local Hilbert space dimension $\textit{q}$ followed by the replica limit $\textit{n}$ → 1, we obtain the critical measurement probability $p_c$ = 1/2 and identify the transition as a bond percolation in the 2D square lattice in this limit. Finally, we show there is no phase transition if the measurements are allowed in an arbitrary nonlocal basis, thereby highlighting the relation between the phase transition and information scrambling. We establish an explicit connection between the entanglement phase transition and the purification dynamics of a mixed state evolution and discuss implications of our results to experimental observations of the transition and simulability of quantum dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Accurate and efficient description of interacting carriers in quantum nanostructures by selected configuration interaction and perturbation theory

In this paper, we present a method to accurately and efficiently calculate many-body states of interacting carriers in quantum nanostructures based on a combination of iterative selection of configurations and perturbation theory. This method enables investigations of large excitonic complexes and multielectron systems with near full configuration interaction accuracy, even though only a small subspace of the full many-body Hilbert space is sampled, thus saving orders of magnitudes in computational resources. Important advantages of this method are that the convergence is controlled by a single parameter, the threshold, and that ground and excited states can be treated on an equal footing. On the example of InAsP nanowire quantum dots described using a million-atom tight-binding approach, we demonstrate the extreme efficiency of the method by numerical studies of large excitonic complexes filling up to the fourth electronic shell. We find that the method generally converges fast as a function of the threshold, profiting from a significant acceleration due to the perturbative corrections. The role of the choice of single-particle basis states is discussed. It is found that the algorithm converges faster in the Hartree-Fock basis only for highly charged systems, where Coulomb repulsion dominates. Finally, based on the observation that second-order perturbative energy corrections only depend on off-diagonal elements of the many-body Hamiltonian, we present a way to accurately calculate many-body states that requires only a relatively small number of Coulomb matrix elements.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Kinetically constrained freezing transition in a dipole-conserving system

Here, we study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fractonlike conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase, where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Quantum many-body scars in a Landau level on a thin torus

We review a kinetically constrained pair-hopping model that arises within a Landau level in the quantum Hall effect. At filling ν = 1/3, the model exactly maps onto the so-called “PXP model,” a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors ν = p/(2p+1), and show that the model is equivalent to nonintegrable spin chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

1-dimensional spin chains↗
DOE OSTI2021

Solving the Bethe-Salpeter equation on a subspace: Approximations and consequences for low-dimensional materials

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation. The repulsive exchange interaction responsible for the singlet-triplet splitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called S approximation [L. X. Benedict, Phys. Rev. B 66, 193105 (2002)PRBMDO0163-182910.1103/PhysRevB.66.193105]. Here, we systematically explore the accuracy of the S approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the S approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamic properties of a polaron coupled to dispersive optical phonons

We study static and dynamic properties of an electron coupled to dispersive quantum optical phonons in the framework of the Holstein model defined on a one-dimensional lattice. Calculations are performed using the Lanczos algorithm based on a highly efficient construction of the variational Hilbert space. Even small phonon dispersion has a profound effect on the low-energy optical response. While the upward phonon dispersion broadens the optical spectra due to single-phonon excitations, the downward dispersion has the opposite effect. With increasing dispersion, a multiphonon excitation (MPE) state becomes the lowest excited state of the system at zero momentum and determines the low-frequency response of the optical conductivity where the threshold for optical absorption moves below the single-phonon frequency. Multiphonon states form a well-defined bandlike feature just above the polaron band as clearly seen in the electron spectral function. Low-energy MPEs should be observable in systems with strong optical phonon dispersion in optical as well as angle-resolved photoemission experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dimerization and spin decoupling in a two-leg Heisenberg ladder with frustrated trimer rungs

We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba 4 Ir 3 O 10 . We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform, yet shows a gapped spinon continuum together with a sharp coherent low-energy branch which renders the system critical overall. In either case, the additional rung spin quickly get sidelined and nearly decouple in the regime when their bare coupling to the ladder is weakened

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Relaxation mechanisms in a disordered system with Poisson-level statistics

Here we discuss the interplay between many-body localization and spin symmetry. To this end, we study the time evolution of several observables in the anisotropic t- j model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom, yet it has smaller Hilbert space and thus allows for numerical studies of larger systems. We compare the field disorder that breaks the $\mathbb{Z}_2$ spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the $\mathbb{Z}_2$ spin transformation relax towards the equilibrium value at relatively short timescales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry-preserving disorder. Odd operators' apparent relaxation is due to their time evolution between distinct symmetry sectors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effective dissipation rate in a Liouvillian-graph picture of high-temperature quantum hydrodynamics

At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that the emergence of this dissipative long-wavelength dynamics from the system's unitary microscopic dynamics is controlled by the structure of the Liouvillian graph of the system's Hamiltonian, that is, the graph induced on Pauli strings by commutation with that Hamiltonian. The Liouvillian graph decomposes naturally into subgraphs of Pauli strings of constant diameter, and the coherent dynamics of these subgraphs determines the rate at which operator weight spreads to long operators. In conclusion, this argument provides a quantitative theory of the emergence of a dissipative effective dynamics from unitary microscopic dynamics; it also leads to an effective model with Hilbert space dimension linear in system size and exponential in the UV cutoff for diffusion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Effective one-band models for the one-dimensional cuprate Ba 2-x Sr x CuO 3+δ

In this work, we consider a multiband Hubbard model H m for Cu and O orbitals in Ba 2-x Sr x CuO 3+δ similar to the three-band model for two-dimensional cuprates. The hopping parameters are obtained from maximally localized Wannier functions derived from ab initio calculations. Using the cell perturbation method, we derive both a generalized t–J model H tJ and a one-band Hubbard model H H to describe the low-energy physics of the system. H tJ has the advantage of having a smaller relevant Hilbert space, facilitating numerical calculations, while additional terms should be included in H H to accurately describe the multiband physics of H m . Using H tJ and the density matrix renormalization group method, we calculate the wave-vector-resolved photoemission and discuss the relevant features in comparison with recent experiments. In agreement with previous calculations, we find that the addition of an attractive nearest-neighbor interaction of the order of the nearest-neighbor hopping shifts the weight from the 3k F to the holon-folding branch. Kinetic effects also contribute to this process.

1-dimensional systems↗
DOE OSTI2024

Quantum fragmentation in the extended quantum breakdown model

We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. Furthermore, our model resembles the breakdown process of particles incident into a cloud chamber with nonzero quantum amplitudes of both exciting and not exciting the local vapor atoms. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially many Krylov subspaces and hence displays nonthermal dynamics. Here, we demonstrate that the fragmentation naturally occurs in an entangled basis and thus provides an example of “quantum fragmentation.” Besides establishing the nature of fragmentation analytically, we also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system. Upon introducing a magnetic field for the spins, most of the Krylov subspaces merge and the model becomes chaotic. Finally, we study the effects of strong randomness on the system and observe behavior similar to that of many-body localized systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Euclidean formulation of relativistic quantum mechanics of N particles

A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at subhadronic distance scales. While direct interaction approaches to relativistic quantum mechanics have proved to be useful, they have two disadvantages. One is that cluster properties are difficult to realize for systems of more than two particles. The second is that the relation to quantum field theories is indirect. Euclidean formulations of relativistic quantum mechanics provide an alternative representation that does not have these difficulties. More surprising, the theory can be formulated entirely in the Euclidean representation without the need for analytic continuation. In this work a Euclidean representation of a relativistic N-particle system is discussed. Kernels for systems of N free particles of any spin are given and shown to be reflection positive. Explicit formulas for generators of the Poincaré group for any spin are constructed and shown to be self-adjoint on the Euclidean representation of the Hilbert space. The structure of correlations that preserve both the Euclidean covariance and reflection positivity is discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

The generator coordinate method begins with the variational construction of a set of nonorthogonal mean-field states that span a subspace of the full many-body Hilbert space. These states are then often projected onto states with good quantum numbers to restore symmetries, leading to a set with members that can be similar to one another, and it is sometimes possible to reduce this set without greatly affecting results. Here, we propose a greedy algorithm that we call the energy-transition-orthogonality procedure (ENTROP) to select subsets of important states. As applied here, the approach selects on the basis of diagonal energy, orthogonality, and contribution to the matrix element that governs neutrinoless double-β decay. We present both shell-model and preliminary ab initio calculations of this matrix element for the decay of 76Ge, with quadrupole deformation parameters and the isoscalar pairing strength as generator coordinates. ENTROP converges quickly, reducing significantly the number of basis states needed for an accurate calculation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗