Search NASA⌕ Search

SEARCH · Search NASA

Results for “Quantum groups”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν ≤ 1 , bounded below by filling factor ν = 1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν = 1 and ν = 3 . The phases near ν = 1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Ding, Jixun K.↗
DOE OSTI2023

Digital quantum simulation of NMR experiments

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Block encodings of discrete subgroups on a quantum computer

We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as BI of S U ( 2 ) and V of S U ( 3 ) . We detail the construction of primitive gates—the inversion gate, the group multiplication gate, the trace gate, and the group Fourier gate—utilizing this encoding method for BT and for the first time BI group. We also provide resource estimations to extract the gluon viscosity. The inversion gates for BT and BI are benchmarked on the quantum computer with estimated fidelities of 40 − 4 + 5 % and 4 − 3 + 5 % , respectively. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Green’s functions on a renormalized lattice: An improved method for the integer quantum Hall transition

Highlights: • Speed up of numerical calculations by exact renormalization group steps. • Practical approach to handle delicate scaling analysis. • Absence of evidence to prefer marginal corrections over power-law corrections. We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green’s function method. We apply this framework to investigate the critical behavior of the integer quantum Hall transition of a tight-binding Hamiltonian defined on a simple square lattice. In addition, we employ an improved scaling analysis that includes two irrelevant exponents to characterize the shift of the critical energy as well as the corrections to the dimensionless Lyapunov exponent. We compare our findings with the results of a conventional implementation of the recursive Green’s function method, and we put them into broader perspective in view of recent development in this field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A numerically exact description of ultrafast vibrational decoherence in vibration-coupled electron transfer

Broadband pump–probe spectroscopy has been widely used to measure vibrational decoherence associated with the reaction coordinate in photoinduced ultrafast vibration-coupled electron transfer (VCET) reactions. These experiments provide insight into the interplay of intramolecular coordinates along the reaction coordinate. However, a general theoretical foundation for analyzing, and even for explaining rigorously, these data is lacking. In this work, we study vibrational decoherence in a model VCET reaction using the nearly exact time-dependent density matrix renormalization group simulation method. We explore how analyzing the density matrix with quantum information measures can help elucidate the evolution of vibrational coherence in simulations of dynamics. We examine how vibrational coherence is affected by electron transfer on the timescale of approximately 100 femtoseconds. Our results suggest that electron transfer, in the nonadiabatic model, changes the vibrational equilibrium position abruptly—an example of a “quantum quench” event. This explains the concomitant vibrational decoherence. We find that abrupt vibrational decoherence can be mitigated by wavepacket motion occurring on the timescale of the electron transfer.

Science & Technology - Other Topics↗
DOE OSTI2023

Atomic-Scale Andreev Probe of Unconventional Superconductivity

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. Furthermore, TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Furthermore, our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Block2 : A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.

Chemistry↗
DOE OSTI2020

Effect of Molecular Structure of Quinones and Carbon Electrode Surfaces on the Interfacial Electron Transfer Process

Quinones can undergo thermodynamically reversible proton-coupled electron transfer reactions and are being applied as electroactive compounds in aqueous organic batteries. However, the electrochemical reversibility of these compounds is affected not only by their molecular structure but also by the properties of a carbon-based electrode surface. This study combines experimental and theoretical approaches to understand this dependence. Specifically, we study the electron transfer kinetics of two synthesized quinone derivatives and two commercially available ones with a glassy carbon, a highly ordered pyrolytic graphite, and a high-edge-density graphite electrode (HEDGE). The electrochemical reversibility is notably improved on the HEDGE, which shows a higher density of defects and presents oxygenated functional groups at its surface. The electron transfer kinetics are controlled by adsorbed species onto the HEDGE. Molecular dynamics simulation and quantum mechanics calculations suggest defects with oxygen-containing functional groups, such as C-O and C$=$O, on HEDGE surfaces drive the interaction with the functional groups of the molecules, during physisorption from van der Waals forces. The presence of sulfonic acid side groups and a greater number of aromatic rings in the molecular structure may contribute to a higher stabilization of quinone derivatives on HEDGEs. We propose that high-performance carbon-based electrodes can be obtained without catalysts for organic batteries, by the engineering of carbon-based surfaces with edge-like defects and oxygenated functional groups.

25 ENERGY STORAGE↗
DOE OSTI2024

Efficient simulation of low-temperature physics in one-dimensional gapless systems

Here, we discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index 0 < q ≤ 1. In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as O⁡(cN 0 ⁢log⁡β) where c is the central charge and N is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Evidence for Dirac flat band superconductivity enabled by quantum geometry

In a flat band superconductor, the charge carriers’ group velocity v F is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors and heavy-fermion systems. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small v F in the conventional Bardeen–Cooper–Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system. Using Schwinger-limited non-linear transport studies we demonstrate an extremely slow normal state drift velocity v n ≈ 1,000 m s –1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid. Importantly, our measurement of superfluid stiffness, which controls the superconductor’s electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution. Here we find evidence for small Cooper pairs, characteristic of the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Magnetism in the two-dimensional dipolar XY model

Here, motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [C. Chen et al., Nature (London) 616, 691 (2023)], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U⁡(1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle S/N≈0.5, close to the one at the critical temperature, S c /N=0.585⁢(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems

The generalized Wigner crystal (GWC) is a novel quantum phase of matter driven by further-range interaction at fractional fillings of a lattice. The role of further-range interaction as the driver for the incompressible state is akin to the Wigner crystal. On the other hand, the significant role of commensurate filling is akin to the Mott insulator. Recent progress in simulator platforms presents unprecedented opportunities to investigate quantum melting in the strongly interacting regime through synergy between theory and experiments. However, the earlier theory literature presents diverging predictions. We study the quantum freezing of GWC through large-scale density matrix renormalization group simulations of a triangular lattice extended Hubbard model. We find a single first-order phase transition between the Fermi liquid and the √3×√3 GWC state. Furthermore, the GWC state shows long-range antiferromagnetic 120° Néel order. Our results present the simplest answers to the question of the quantum phase transition into the GWC phase and the properties of the GWC phase.

Density matrix renormalization group↗
DOE OSTI2020

A multilayer multi-configurational approach to efficiently simulate large-scale circuit-based quantum computers on classical machines

Here, a multilayer multi-configurational theory framework is adapted to simulate circuit-based quantum computers. Quantum addition of superpositions of an exponential number of summands is performed in polynomial time with high accuracy. We demonstrate numerically accurate calculations including up to one million qubits for entangling benchmarks. Simulation cost can be assessed by entropy-based entanglement measures. For the considered systems, we show that the entanglement only grows weakly with the system size. The present simulations demonstrate how quantum algorithms in low-entropy regimes can be used efficiently on classically simulated quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Novel Wavefunction Approaches for Studying Actinides and Other Heavy Elements (Final Report (2012-2020))

The theoretical characterization of actinide molecules is a crucial complement to their experimental study; actinides are vital to issues of national security and energy, but they are expensive and hazardous to study experimentally. However, because actinides contain a large number of electrons and are often strongly correlated, their theoretical description is difficult. We have had success studying actinide chemistry and physics using density functional theoretical approaches over the past several years, but we have found that such methods are incapable of treating strong correlations adequately. We thus shifted our research focus to the development of tractable wavefunction methods for strong correlations of actinides. Our early wavefunction-based approaches focused on extending symmetry-adapted, single-reference coupled cluster for treating strong correlations with feasible computational cost. While we have had some success along these lines, we have recently developed spin-projected unrestricted coupled cluster, which is essentially a black-box multi-reference coupled cluster theory that is superior to unrestricted coupled cluster for small- to medium-sized systems across practically all physical correlation strengths, yet preserves good quantum numbers. For actinides, however, where spin-orbit coupling is often nonnegligible, spin is no longer a fundamental symmetry. We thus propose to develop time reversal and point group projected coupled cluster, which will preserve the fundamental symmetries for actinides. Time reversal projection is achieved via the product of half-spin projection, or spin flip, and complex conjugation projection. Along with point group, these are discrete symmetries, i.e. non-continuous quantum numbers, which, in addition to being the correct symmetries for actinides, can be implemented in lower computational cost than full spin projection. We propose the development of these theories within a synergistic collaboration to use the new methods to elucidate difficult actinide chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Conformal field theories are magical

“Magic” is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z 3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q = 3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. Here, we explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT.

1-dimensional spin chains↗
DOE OSTI2025

Towards absolutely stable ergodicity breaking in two and three dimensions

We propose physically reasonable systems capable of avoiding ergodicity at infinite time in the thermodynamic limit, even with generic perturbations and when coupled to a heat bath. In two dimensions, the rainbow loop soup has (stretched) exponentially numerous absolutely stable nonergodic states with diverging energy but vanishing energy density. In three dimensions the rainbow membrane soup has (stretched) exponentially numerous nonergodic states with diverging energy barriers, leading to infinite-time robust ergodicity breaking that even survives coupling to a nonzero temperature heat bath. We describe our results in the language of exact emergent symmetries and demonstrate how the systems avoid common instabilities. Furthermore, our construction naturally connects to quantum dimer models, topologically ordered systems, the group word construction, and Hamiltonians whose low-energy eigenstates exhibit anomalous entanglement entropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains

Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. Here, we establish a rigorous quantum-classical correspondence between the “giant quasiparticles” that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.

1-dimensional spin chains↗