A stabilization mechanism for many-body localization in two dimensions

Abstract

Experiments in cold atom systems see almost identical signatures of many body localization (MBL) in both one-dimensional ($d=1$) and two-dimensional ($d=2$) systems despite the thermal avalanche hypothesis showing that the MBL phase is unstable for $d>1$. Underpinning the thermal avalanche argument is the assumption of exponential localization of local integrals of motion (LIOMs). In this work we demonstrate that addition of a confining potential -- as is typical in experimental setups -- allows a non-interacting disordered system to have super-exponentially (Gaussian) localized wavefunctions, and an interacting disordered system to undergo a localization transition. Moreover, we show that Gaussian localization of MBL LIOMs shifts the quantum avalanche critical dimension from $d=1$ to $d=2$, potentially bridging the divide between the experimental demonstrations of MBL in these systems and existing theoretical arguments that claim that such demonstrations are impossible.

References in corpus (13)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Constructing local integrals of motion in the many-body localized phase
• Homogeneous Atomic Fermi Gases
• How a small quantum bath can thermalize long localized chains
• Challenges to observation of many-body localization
• Markovian baths and quantum avalanches
• Possible experimental manifestations of the many-body localization
• Many body localization with long range interactions
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?

Cited by in corpus (7)

• Many-Body Localization in the Age of Classical Computing
• Observation of many-body Fock space dynamics in two dimensions
• Catching thermal avalanches in the disordered XXZ model
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Thermal avalanches in isolated many-body localized systems
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Quantum Avalanches in ${\mathbb{Z}}_2$-preserving Interacting Ising Majorana Chain