Phase Thermalization: from Fermi Liquid to Incoherent Metal

TL;DR

This paper demonstrates that phase thermalization, where a probe acquires the phase of a bath, can occur even when the probe and bath are described by different Hamiltonians, exemplified by a Majorana chain system.

Contribution

It provides an explicit example of phase thermalization between a Fermi liquid probe and an incoherent metal bath with different microscopic Hamiltonians.

Findings

Probe becomes an incoherent metal at low energies.

Lyapunov spectrum matches between probe and bath.

Diffusion coefficient is identical for probe and bath.

Abstract

When a system consists of a large subsystem (bath) and a small one (probe), thermalization implies induction of temperature of the bath onto the probe. If both the bath and the probe are described by same microscopic Hamiltonian, thermalization further entails that the probe imbibes the phase of the bath. We refer to this phenomenon as {\it phase thermalization}. However, it is not clear whether this phenomenon is realizable when the probe and the bath are described by different microscopic Hamiltonians. We show {\it phase thermalization} is possible even when the microscopic Hamiltonians differ significantly. We provide an explicit example, where the probe is a Fermi liquid realized by a Majorana chain with $n \gg 1$ fermions per site interacting through random hopping and the bath is an incoherent metal described by another Majorana chain with $N > n$ fermions per site interacting through arbitrarily long range random four-fermion interaction. In deep infrared (\emph{i.e.} at very low energies), the probe turns into an incoherent metal, with Lyapunov spectrum and diffusion coefficient identical to the bath.