Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2002.05549 · Physical Review A

Semiclassical dynamics of a disordered two-dimensional Hubbard model with long-range interactions

Adam S. Sajna, Anatoli Polkovnikov

Published Sep 28, 2020• 13 citations
arXivHTMLPDF

Abstract

Quench dynamics in a two-dimensional system of interacting fermions is analyzed within the semiclassical truncated Wigner approximation (TWA). The models with short-range and long-range interactions are considered. We show that in the latter case, the TWA is very accurate, becoming asymptotically exact in the infinite-range limit, provided that the semiclassical Hamiltonian is correctly identified. Within the TWA, different dynamical timescales of charges and spins can be clearly distinguished. Interestingly, for a weak and moderate disorder strength, we observe subdiffusive behavior of charges, while spins exhibit diffusive dynamics. At strong disorder, the quantum Fisher information shows logarithmic growth in time with a slower increase for charges than for spins. It is shown that in contrast to the short-range model, strong inhomogeneities such as domain walls in the initial state can significantly slow down thermalization dynamics, especially at weak disorder. This behavior can put additional challenges in designing cold-atom experimental protocols aimed to analyze possible many-body localization in such systems. While within this approach we cannot make any definite statements about the existence of a many-body localized phase, we see a very fast crossover as a function of disorder strength from rapidly thermalizing to a slow glassylike regime both for the short-range and long-range models.

DOI
10.1103/physreva.102.033338

Related papers

Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials

Aleksander Kaczmarek, Adam S. Sajna

The quench dynamics of the Hubbard model in tilted and harmonic potentials is discussed within the semiclassical picture. Applying the fermionic truncated Wigner approximation (fTWA), the dynamics of imbalances for charge and spin degrees of freedom is analyzed and its time evolution is compared with the exact simulations in a one-dimensional lattice. Quench from charge or spin density waves is considered. We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. Such an improvement of fTWA is also obtained for the higher-order correlations in terms of quantum Fisher information for charge and spin channels. This allows us to discuss the dynamics of larger system sizes and connect our discussion to the recently introduced Stark many-body localization. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt results in subdiffusive dynamics, similar to that of disordered systems. Moreover, for specific values of harmonic potential, we observed phase separation of ergodic and nonergodic regions in real space. The latter fact is especially important for ultracold-atom experiments in which harmonic confinement can be easily imposed, causing a significant change in relaxation times for different lattice locations.

arXiv:2210.01082•Physical review. B./Physical review. B•Oct 9, 2023•5 citations

Semiclassical bounds on the dynamics of two-dimensional interacting disordered fermions

Łukasz Iwanek, Marcin Mierzejewski, Anatoli Polkovnikov +2 more

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$ noise at strong disorder.

arXiv:2209.15062•Physical review. B./Physical review. B•Feb 8, 2023•6 citations

Many body localization in Disordered One-Dimensional Fermi-Hubbard Model

Harmanjeet Kaur, Vinod Ashokan

We investigate the non-equilibrium dynamics of the disordered one-dimensional Fermi-Hubbard model with a focus on many-body localization. The system is initialized in a charge-density-wave-state, and its time evolution is analyzed through sublattice imbalance (spin and charge), and bipartite entanglement entropy. A clear crossover from ergodic to non-ergodic behavior is observed with increasing disorder strength. In the weak disorder regime, rapid decay of imbalance and the fast growth of entanglement indicate efficient thermalization. In contrast, a strong disorder leads to persistent imbalance and slow dynamics, signaling the breakdown of ergodicity. The charge and spin sectors exhibit distinct relaxation behavior, providing evidence for partial decoupling between these degrees of freedom. Furthermore, in the interacting regime, the entanglement entropy shows slow logarithmic growth, reflecting the dephasing-driven dynamics characteristic of the many-body localized phase. These results highlight the interplay between disorder and interactions in determining the dynamical properties of the system and establish robust signatures of many-body localization in the Fermi-Hubbard model.

arXiv:2606.04948•Jun 3, 2026•0 citations

Exploring many-body localization and thermalization using semiclassical methods

Oscar L. Acevedo, Arghavan Safavi-Naini, Johannes Schachenmayer +3 more

The discrete truncated Wigner approximation (DTWA) is a semiclassical phase-space method useful for the exploration of many-body quantum dynamics. In this work we investigate many-body localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a one-dimensional random field Heisenberg spin chain with short-range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long-range interactions and/or systems in higher dimensions.

arXiv:1705.03107•Physical Review A•Sep 5, 2017•36 citations

Slow dynamics in a two-dimensional Anderson-Hubbard model

Yevgeny Bar Lev, David R. Reichman

We study the real-time dynamics of a two-dimensional Anderson-Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite-size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible timescales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold-atoms experiments.

arXiv:1508.05391•Europhysics Letters (EPL)•Feb 1, 2016•63 citations

Universal semiclassical dynamics in disordered two-dimensional systems

Łukasz Iwanek, Marcin Mierzejewski, Anatoli Polkovnikov +2 more

The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/{\ensuremath{\xi}}_{W}$, where in two dimensions the timescale ${\ensuremath{\xi}}_{W}$ follows a stretched-exponential dependence on disorder strength.

arXiv:2409.12956•Physical review. B./Physical review. B•Mar 20, 2025•0 citations
Quench dynamics in a two-dimensional system of interacting fermions is analyzed within the semiclassical truncated Wigner approximation (TWA). The models with short-range and long-range interactions are considered. We show that in the latter case, the TWA is very accurate, becoming asymptotically exact in the infinite-range limit, provided that the semiclassical Hamiltonian is correctly identified. Within the TWA, different dynamical timescales of charges and spins can be clearly distinguished. Interestingly, for a weak and moderate disorder strength, we observe subdiffusive behavior of charges, while spins exhibit diffusive dynamics. At strong disorder, the quantum Fisher information shows logarithmic growth in time with a slower increase for charges than for spins. It is shown that in contrast to the short-range model, strong inhomogeneities such as domain walls in the initial state can significantly slow down thermalization dynamics, especially at weak disorder. This behavior can put additional challenges in designing cold-atom experimental protocols aimed to analyze possible many-body localization in such systems. While within this approach we cannot make any definite statements about the existence of a many-body localized phase, we see a very fast crossover as a function of disorder strength from rapidly thermalizing to a slow glassylike regime both for the short-range and long-range models.
The quench dynamics of the Hubbard model in tilted and harmonic potentials is discussed within the semiclassical picture. Applying the fermionic truncated Wigner approximation (fTWA), the dynamics of imbalances for charge and spin degrees of freedom is analyzed and its time evolution is compared with the exact simulations in a one-dimensional lattice. Quench from charge or spin density waves is considered. We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. Such an improvement of fTWA is also obtained for the higher-order correlations in terms of quantum Fisher information for charge and spin channels. This allows us to discuss the dynamics of larger system sizes and connect our discussion to the recently introduced Stark many-body localization. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt results in subdiffusive dynamics, similar to that of disordered systems. Moreover, for specific values of harmonic potential, we observed phase separation of ergodic and nonergodic regions in real space. The latter fact is especially important for ultracold-atom experiments in which harmonic confinement can be easily imposed, causing a significant change in relaxation times for different lattice locations.
Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous 1/f1/f1/f noise at strong disorder.
We investigate the non-equilibrium dynamics of the disordered one-dimensional Fermi-Hubbard model with a focus on many-body localization. The system is initialized in a charge-density-wave-state, and its time evolution is analyzed through sublattice imbalance (spin and charge), and bipartite entanglement entropy. A clear crossover from ergodic to non-ergodic behavior is observed with increasing disorder strength. In the weak disorder regime, rapid decay of imbalance and the fast growth of entanglement indicate efficient thermalization. In contrast, a strong disorder leads to persistent imbalance and slow dynamics, signaling the breakdown of ergodicity. The charge and spin sectors exhibit distinct relaxation behavior, providing evidence for partial decoupling between these degrees of freedom. Furthermore, in the interacting regime, the entanglement entropy shows slow logarithmic growth, reflecting the dephasing-driven dynamics characteristic of the many-body localized phase. These results highlight the interplay between disorder and interactions in determining the dynamical properties of the system and establish robust signatures of many-body localization in the Fermi-Hubbard model.
The discrete truncated Wigner approximation (DTWA) is a semiclassical phase-space method useful for the exploration of many-body quantum dynamics. In this work we investigate many-body localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a one-dimensional random field Heisenberg spin chain with short-range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long-range interactions and/or systems in higher dimensions.
We study the real-time dynamics of a two-dimensional Anderson-Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite-size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible timescales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold-atoms experiments.
The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/{\ensuremath{\xi}}_{W}$, where in two dimensions the timescale ${\ensuremath{\xi}}_{W}$ follows a stretched-exponential dependence on disorder strength.