Many-Body Delocalization via Emergent Symmetry

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 Z2 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. The presented ideas raise the possibility of an 'inverted quantum scar', in which a state that does not exhibit area law entanglement is embedded in an MBL spectrum, which does.

Escaping many-body localization in an exact eigenstate

“…For both the uniform δ = 0 and disordered δ = 3 system, the Rényi entropy follows Eq. (11). Without disorder, the fit y = 0.247x + 1.88 agrees with the expected slope C = 0.25.…”

“…While emergent symmetry has previously been identified as a mechanism to obtain weak violation of MBL [11], we have here shown that weak violation of MBL can also happen without the presence of emergent symmetry. Specifically, we have constructed a model with a known eigenstate.…”

“…Recently, it was found that one can also construct Hamiltonians with non-MBL eigenstates embedded in a sea of MBL eigenstates [11]. This can be achieved by utilizing the incompatibility between MBL and non-Abelian symmetries [12,13].…”

“…This can be achieved by utilizing the incompatibility between MBL and non-Abelian symmetries [12,13]. Specifically, a Hamiltonian was developed hosting a special eigenstate with emergent SU(2) symmetry [11], i.e. the eigenstate had SU(2) symmetry although the Hamiltonian did not.…”

“…In the uniform system, δ = 0, the fit is given by y = 0.247x + 1.88, and the slope agrees with the constant C = 0.25. For the disordered system δ = 3, the data follows equation (11) with the linear fit given by y = 0.107x + 0.893. We obtain a similar value for the slope for a system with N = 60 sites, and hence we do not expect the slope to change with system size.…”