[Paper Review] Stark many-body localization with long-range interactions

Xiangping Jiang, Rui Qi+3 more|arXiv (Cornell University)|Jul 23, 2023

Quantum many-body systemsPhysics and Astronomy3 citations

TL;DR

This study investigates Stark many-body localization (MBL) in one-dimensional spinless fermion systems with long-range (LR) interactions, using mean gap ratio and many-body inverse participation ratio to map phase diagrams. It reveals that strong LR interactions induce Hilbert-space fragmentation, leading to robust Stark MBL independent of linear potential strength—contrasting with short-range interactions where symmetry exists between weak and strong interaction limits.

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.

Motivation & Objective

• To understand the role of interaction strength in Stark many-body localization (MBL) in disorder-free, one-dimensional spinless fermion systems with long-range interactions.
• To determine whether strong long-range interactions preserve or destroy the MBL phase, especially in comparison to short-range interactions.
• To investigate the ergodic-to-Stark MBL transition by analyzing spectral statistics and dynamical observables such as imbalance and entanglement entropy.
• To examine how initial state preparation affects dynamics, probing the role of Hilbert-space fragmentation in preventing thermalization.
• To establish a comprehensive phase diagram for Stark MBL in the presence of long-range interactions, contrasting it with short-range interaction behavior.

Proposed method

• Numerical computation of the mean gap ratio ⟨r⟩ and many-body inverse participation ratio (MIPR) ⟨I⟩ to distinguish between ergodic and localized phases in finite-size systems.
• Use of the time-dependent variational principle (TDVP) with matrix product states to simulate real-time dynamics of density imbalance and von Neumann entanglement entropy.
• Study of half-filling spinless fermion systems under a linear potential (Stark field) with both short-range (SR) and long-range (LR) interactions, parameterized by interaction decay exponent α.
• Analysis of spectral statistics and entanglement scaling to identify ergodic (volume-law) vs. localized (area-law) behavior in eigenstates.
• Comparison of dynamical responses under different initial states (Néel, SDW, DDW) to probe sensitivity to initial conditions and identify non-ergodic dynamics.
• Employment of QuSpin and ITensor libraries for exact diagonalization (ED) and TDVP simulations, respectively, on systems of size L=16–20.

Experimental results

Research questions

• RQ1 How does the strength of long-range interactions affect the stability of Stark many-body localization in one-dimensional, disorder-free fermionic systems?
• RQ2 Is there a qualitative symmetry between weak and strong interaction limits in the presence of long-range interactions, as observed in short-range interacting systems?
• RQ3 To what extent do long-range interactions induce Hilbert-space fragmentation, and how does this affect thermalization and dynamical observables?
• RQ4 How do the dynamics of entanglement entropy and density imbalance depend on initial state preparation in the presence of strong long-range interactions?
• RQ5 Can a robust Stark MBL phase persist even when the linear potential strength is varied, under strong long-range interactions?

Key findings

• For short-range interactions, a qualitative symmetry exists between weak and strong interaction limits in the Stark MBL phase diagram, as indicated by symmetric ⟨r⟩ and ⟨I⟩ behavior.
• In contrast, long-range interactions break this symmetry: the system remains in a Stark MBL phase for all linear potential strengths when interactions are strong.
• Strong long-range interactions induce Hilbert-space fragmentation, which prevents thermalization and leads to persistent localization regardless of the Stark field strength.
• Dynamical simulations show that entanglement entropy dynamics are highly sensitive to initial state preparation, with distinct behaviors for Néel, SDW, and DDW states.
• In the strongly interacting regime, entanglement entropy exhibits a significant slowdown and approaches a finite value at long times for both SR and LR cases, but only LR systems show this behavior uniformly across all potential strengths.
• For strong long-range interactions, the entanglement entropy remains finite and non-ergodic for all field strengths γ, indicating a robust Stark MBL phase independent of the linear potential.