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Results for “exactly solvable models”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

States of strongly interacting particles are of fundamental interest in physics and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model short-range interaction that is infinitely strong compared to the cyclotron energy. Here, we demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors v<1/2p and produces a fractional quantum Hall effect at fractions of the form v=n/(2pn+1), where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Exactly solvable model of light-scattering errors in quantum simulations with metastable trapped-ion qubits

Here, we analytically solve a model for light scattering in Ising dynamics of metastable atomic qubits, generalizing the approach of Foss-Feig et al. to include leakage outside the qubit manifold. We analyze the influence of these fundamental errors in simulations of proposed experiments with metastable levels of 40 Ca + ions in a Penning trap. We find that “effective magnetic fields” generated by leaked qubits have significant impacts on spin-spin correlation functions for Greenberger-Horne-Zeilinger state preparation or for quantum simulations with strong coupling, while spin squeezing uses a much weaker coupling and is largely insensitive to the simulated leakage errors, even with a few hundred ions. Our theory and results are expected to be useful in modeling a variety of metastable qubit experiments in the future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Developing new and understanding old approximations in TDDFT

When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, and sometimes even quantitative predictions. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange–correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn–Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange–correlation potential from a coupling-constant path integration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Nonadiabatic transitions during a passage near a critical point

The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although the system is passing slowly very close to it. Here, we show that the leading exponent for the excitation probability can then be obtained by standard arguments of the Dykhne formula, but the exponential prefactor is no longer simple and behaves as a power law on the characteristic transition rate. We derive this prefactor for the nonlinear Landau–Zener model by adjusting Dykhne’s approach. Then, we introduce an exactly solvable model of the transition near a critical point in the Stark ladder. We derive the number of excitations for it without approximations and find qualitatively similar results for the excitation scaling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Energy-momentum tensor in a classical model of the electron

We show that the leading nonanalytic terms in the small-𝑡 expansion of the energy-momentum tensor form factors of an electrically charged particle in QED can be correctly derived in a classical model of the electron by Białynicki-Birula. Based on the lucidity of the employed exactly solvable model, we comment also on the recently proposed concept of a regularized proton 𝐷-term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Integrable model of topological SO(5) superfluidity

Assisted by general symmetry arguments and a many-body invariant, we introduce a phase of matter that constitutes a topological SO(5) superfluid. Key to this finding is the realization of an exactly solvable model that displays some similarities with a minimal model of superfluid 3 He. We study its quantum phase diagram and correlations, and find exotic superfluid as well as metallic phases in the repulsive sector. At the critical point separating trivial and nontrivial superfluid phases, our Hamiltonian reduces to the globally SO(5)-symmetric Gaudin model with a degenerate ground manifold that includes quartet states. Most importantly, the exact solution permits uncovering of an interesting non-pair-breaking mechanism for superfluids subject to external magnetic fields. Furthermore, nonintegrable modifications of our model lead to a strong-coupling limit of our metallic phase with a ground-state manifold that shows an extensive entropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Topological phase transition without single particle gap closing in strongly correlated systems

Here, in this study, we show two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

Highlights: • System–environment quantum correlation: a main solid state NMR decoherence channel. • Non-separable system–environment model yields realistic spin decoherence rates. • New open quantum system approach explains irreversible decay of refocused NMR echoes. • Adiabatic quantum decoherence is inherently irreversible and eigen-selective. This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dynamical phase transitions in models of collective neutrino oscillations

Collective neutrino oscillations can potentially play an important role in transporting lepton flavor in astrophysical scenarios where the neutrino density is large, typical examples are the early universe and supernova explosions. It has been argued in the past that simple models of the neutrino Hamiltonian designed to describe forward scattering can support substantial flavor evolution on very short timescales t ≈ log(N) / (G Fρν ), with N the number of neutrinos, G F the Fermi constant and ρ ν the neutrino density. This finding is in tension with results for similar but exactly solvable models for which t ≈ √N/(G Fρν ) instead. In this work we provide a coherent explanation of this tension in terms of dynamical phase transitions (DPT) and study the possible impact that a DPT could have in more realistic models of neutrino oscillations and their mean-field approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Some exactly solvable and tunable frustrated spin models

In this report we discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain’s fully frustrated model, which interpolates between Onsager’s 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions a lá Bethe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

The range of non-Kitaev terms and fractional particles in α-RuCl 3

Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of α-RuCl 3 with quantum Monte Carlo (QMC) results for the Kitaev QSL. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Renormalization of states and quasiparticles in many-body downfolding

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We show that the renormalization factor provides a unique measure of the quality of the compression as it directly represents the projection between the approximate stationary state of the many-body Hamiltonian and the full many-body wavefunction. Hence, the renormalization factor is a measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [Romanova et al., npj Comput. Mater. 9, 126 (2023)], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and their environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.

Green-functions technique↗
DOE OSTI2022

Fractionalization of subsystem symmetries in two dimensions

The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z 2 topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

2-dimensional systems↗
DOE OSTI2022

Determination of asymptotic normalization coefficients for the channel 16 O→ α+ 12 C: excited state 16 O(0 + ; 6.05 MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC C for the virtual decay 16 O(0 + ; 6.05 MeV)→ α+ 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm -1/2 . The ANC C is found by analytic continuation in energy of the α 12 C s-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the 16O bound state and lying in the unphysical region of negative energies. To determine C, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC C is found by solving the Schrödinger equation for the two-body α 12 C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of 16 O(0 + ; 6.05 MeV) in the α+ 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm -1/2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

In this work we propose a \mathbb{Z}_N ℤ N clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with N^2 N 2 (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

Delfino, Guilherme↗
DOE OSTI2024

Pairing tendencies in the doped Kitaev-Heisenberg model

Here, we study the impact of hole doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a t - J - K model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the Néel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely, a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Dynamics of fractionalized mean-field theories: Consequences for Kitaev materials

There have been substantial recent efforts, both experimentally and theoretically, to find a material realization of the Kitaev spin liquid—the ground state of the exactly solvable Kitaev model on the honeycomb lattice. Candidate materials are now plentiful, but the presence of non-Kitaev terms makes comparison between theory and experiment challenging. Here, we rederive time-dependent Majorana mean-field theory and extend it to include quantum phase information, allowing the direct computation of the experimentally relevant dynamical spin-spin correlator, which reproduces exact results for the unperturbed model. In contrast to previous work, we find that small perturbations do not substantially alter the exact result, implying that α-RuCl 3 is perhaps farther from the Kitaev phase than originally thought. Our approach generalizes to any correlator and to any model where Majorana mean-field theory is a valid starting point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗