Many-Body Delocalization via Emergent Symmetry

N S Srivatsa,Roderich Moessner,Anne E B Nielsen

doi:10.1103/physrevlett.125.240401

N S Srivatsa, Roderich Moessner + Show 1 more

Open Access

https://doi.org/10.1103/physrevlett.125.240401

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Abstract

Many-body localization (MBL) provides a mechanism to avoid thermalization in many-body quantum systems. Here, we show that an emergent symmetry can protect a state from MBL. Specifically, we propose a Z_{2} symmetric model with nonlocal interactions, which has an analytically known, SU(2) invariant, critical ground state. At large disorder strength, all states at finite energy density are in a glassy MBL phase, while the lowest energy states are not. These do, however, localize when a perturbation destroys the emergent SU(2) symmetry. The model also provides an example of MBL in the presence of nonlocal, disordered interactions that are more structured than a power law. Finally, we show how the protected state can be moved into the bulk of the spectrum.

Highlights

The eigenstate thermalization hypothesis suggests that clean quantum systems typically thermalize [1,2]
While it is known that Many-body localization (MBL) can be present in systems where the Hamiltonian has Z2 symmetry [7], it has been argued that Hamiltonians with SU(2) symmetry cannot support a MBL phase, because the eigenstates of such Hamiltonians do not have area law entanglement [8,9,10]
Recent studies, which have focused on power law interactions and/or hopping in a random potential or random magnetic field, suggest that MBL can occur in long-range models [12,13,14,15]

Summary

Introduction

The eigenstate thermalization hypothesis suggests that clean quantum systems typically thermalize [1,2]. We introduce disorder into this model, and we show that all states at finite energy density form a glassy phase [5,7,18] at an appropriate disorder strength, while the ground state remains critical. For a wide range of disorder strengths all the states at finite energy density form a MBL glass, while a few states at the bottom of the spectrum do not.

Results

Conclusion