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arXiv:2307.12376

Stark many-body localization with long-range interactions

Xiangping Jiang, Rui Qi, Yang Sheng, Yayun Hu, Guangwen Yang

Published Jul 23, 2023• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.2307.12376

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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.
Many-body localization (MBL), a transportless phase in disordered interacting quantum systems, has recently been observed in systems without disorder but instead with a strong linear potential, a phenomenon known as Stark MBL. Here, the authors show how several experimental setups devised to study conventional MBL can also be used for Stark MBL, due to their almost identical phenomenologies. They then discuss Stark MBL as a possible experimental setting to explore Hilbert space fragmentation in systems with conserved dipole moment.
We study theoretical transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria characterizing localization, we construct effective phase diagrams for several types of lattice systems with variable amplitude of the external linear tilt and interaction strength. By means of exact diagonalization and time-dependent variational principle numerical approaches we analyze system dynamics after quenches. Our results reveal that the Stark localization without any artificial source of disorder remains stable upon inclusion of long-range interactions.
We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.
The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.
We discuss properties of interacting spinless fermions in a tilted optical lattice as modeled by Heisenberg spin chain in magnetic (or electric) field changing linearly across the chain. The system shows genuine features of strong localization for a sufficiently large tilt with distinct features different from disorder induced localization. In particular, Stark many-body localization is characterized in time dynamics by a linear increase of the entanglement entropy followed by a saturation at a constant, time independent value -- both the number (classical) and the configuration (quantum) entropies saturate to a constant value. Similarly, the correlation with the initial state (the so called imbalance) stabilizes at a constant value (modulo large fluctuations coming from short time Bloch-type oscillations). The presence of an additional harmonic potential profoundly affects the dynamics of the model -- its behavior resembles standard MBL characteristics -- the logarithmic growth of the entanglement entropy in particular. In that case, we find strong revival phenomena associated with the manifold of equally spaced states, degenerate in the absence of the harmonic potential.
Stark Many-Body Localization (MBL) is a phenomenon observed in quantum systems in the absence of disorder, where the presence of a linear potential, known as the Stark field, causes the localization. Our study aims to provide novel insight into the properties of Stark MBL and to discover unique entanglement characteristics specific to this phenomenon. The phase diagram analysis reveals different behavior with varying interaction strengths. Furthermore, we highlight the influence of domain wall structures on the breakdown of the entanglement entropy of the system. Moreover, the investigation of Out-of-Time-Ordered Correlator (OTOC) behavior demonstrates distinct responses to interactions based on domain wall configurations. Our findings contribute to a better understanding of Stark MBL and offer valuable insights into the entanglement properties of systems subjected to Stark potentials.