Long range interaction and breakdown of many-body localization

We present a theoretical and numerical study of the many-body localization (MBL) transition and entanglement dynamics in disordered spin-fermion chains with long-range interactions. Moving beyond standard single-particle pictures, we investigate the breakdown of ergodicity and thermalization by constructing an effective Hamiltonian via iterative Schrieffer-Wolff transformations and utilizing the local integrals of motion (l-bits) formalism. Our analysis examines entanglement entropy growth, level spacing statistics, and the transition from Wigner-Dyson to Poisson statistics. Furthermore, we derive analytical estimates for the dephasing rate scaling as a function of long-range potential parameters and validate the theoretical findings using exact diagonalization (ED) numerical protocols with finite-size scaling.We present a theoretical and numerical study of the many-body localization (MBL) transition and entanglement dynamics in disordered spin-fermion chains with long-range interactions. Moving beyond standard single-particle pictures, we investigate the breakdown of ergodicity and thermalization by constructing an effective Hamiltonian via iterative Schrieffer-Wolff transformations and utilizing the local integrals of motion (l-bits) formalism. Our analysis examines entanglement entropy growth, level spacing statistics, and the transition from Wigner-Dyson to Poisson statistics. Furthermore, we derive analytical estimates for the dephasing rate scaling as a function of long-range potential parameters and validate the theoretical findings using exact diagonalization (ED) numerical protocols with finite-size scaling.

Sep 22, 20260 citations

Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

Alexander L. Burin

Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping $V(R)\ensuremath{\propto}{R}^{\ensuremath{-}\ensuremath{\alpha}}$ always leads to the localization breakdown in a thermodynamic limit of an infinite system at $\ensuremath{\alpha}<3d/2$ where $d$ is a system dimension. The delocalization takes place due to the induced Ising interactions $U(R)\ensuremath{\propto}{R}^{\ensuremath{-}2\ensuremath{\alpha}}$ of ``extended'' resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring $\ensuremath{\alpha}\ensuremath{\ge}2d$ which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping $V(R)\ensuremath{\propto}{R}^{\ensuremath{-}\ensuremath{\alpha}}$ always leads to the localization breakdown in a thermodynamic limit of an infinite system at $\ensuremath{\alpha}<3d/2$ where $d$ is a system dimension. The delocalization takes place due to the induced Ising interactions $U(R)\ensuremath{\propto}{R}^{\ensuremath{-}2\ensuremath{\alpha}}$ of ``extended'' resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring $\ensuremath{\alpha}\ensuremath{\ge}2d$ which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.

arXiv:1503.06508Physical Review BSep 25, 201597 citations

Dynamics close to the many-body localization transition

Yevgeny Bar Lev, David R. Reichman

Bulletin of the American Physical SocietyMar 4, 20140 citations

Origin and Emergent Features of Many-Body Dynamical Localization

Ang Yang, Zekai Chen, Yanliang Guo +3 more

Physical Review LettersMar 9, 20261 citation

Stark many-body localization with long-range interactions

Xiangping Jiang, Rui Qi, Yang Sheng +2 more

In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.

arXiv:2307.12376Jul 23, 20231 citation

d

is a system dimension. The delocalization takes place due to the induced Ising interactions $U(R)\ensuremath{\propto}{R}^{\ensuremath{-}2\ensuremath{\alpha}}$ of ``extended'' resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring $\ensuremath{\alpha}\ensuremath{\ge}2d$ which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.