Criterion for Many-Body Localization-Delocalization Phase Transition

By Maksym Serbyn, Z. Papi'c, D. Abanin. 2015

234 citations recorded by the source corpus.

We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system’s eigenstates, finding a qualitatively different behavior in the many-body localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter G(L)=⟨ln(Vnm/δ)⟩, which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter G(L) decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when G(L) is independent of system size, G(L)=Gc∼1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1/2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3521e18f0141cb693e28b359ad818ac8f8af3e5b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Tomaz Prosen
2. L. Vidmar
3. D. Abanin
4. J. Moore
5. J. Bonvca
6. Jan vSuntajs
7. Maksym Serbyn
8. Z. Papi'c

In Condensed Matter Physics

1. Tomaz Prosen
2. J. Moore
3. L. Vidmar
4. J. Bonvca
5. Jan vSuntajs
6. D. Abanin
7. Maksym Serbyn
8. Z. Papi'c

In Statistical and Nonlinear Physics

1. Tomaz Prosen
2. J. Moore
3. Maksym Serbyn
4. L. Vidmar
5. J. Bonvca
6. Jan vSuntajs
7. D. Abanin
8. Z. Papi'c

Citations in the corpus

• Spectral statistics across the many-body localization transition (2015, methodology): “We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements.”
• Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations (2018, background): “We note that the ETH ansatz (7) for the matrix elements has been verified in several low-dimensional models [16,51–53], while it was found to break down in many-body localized systems [54,55].”
• Ergodicity breaking transition in finite disordered spin chains (2020, methodology): “[65] M.”