Many-body localization near the critical point

Abstract

We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough $\text{qualitative}$ level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\nu \to \infty$, but the divergence is weaker than for the KT transition.

11 pages, 1 figure; published in Physical Review B

References in corpus (12)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Many-body localization edge in the random-field Heisenberg chain
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Constructing local integrals of motion in the many-body localized phase
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• How a small quantum bath can thermalize long localized chains
• Renormalization-group study of the many-body localization transition in one dimension
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Are many-body localized systems stable in the presence of a small bath?
• A microscopically motivated renormalization scheme for the MBL/ETH transition

Cited by in corpus (6)

• Stark many-body localization: Evidence for Hilbert-space shattering
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• Characterizing the many-body localization transition through correlations
• Localization dynamics in a centrally coupled system
• Many-body localization in a tilted potential in two dimensions