Relaxation to an Ideal Chern Band through Coupling to a Markovian Bath

TL;DR

This paper introduces a microscopic mechanism where coupling to a Markovian bath causes generic Chern bands to relax into ideal bands, facilitating the stabilization of fractional Chern insulators.

Contribution

It demonstrates, through theoretical modeling and numerical simulation, how weak coupling to an Ohmic bath drives Chern bands toward ideal topological properties.

Findings

Berry curvature and quantum metric co-evolve to saturation.

Numerical simulations validate the relaxation mechanism.

Provides a dissipative route to realize ideal Chern bands.

Abstract

We propose a microscopic, weak-coupling mechanism by which generic Chern bands relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leggett like Ohmic bosonic bath. Using the Born-Markov approximation, Slater determinant states of a Chern band under Hartree-Fock approximation evolve toward Slater determinant states corresponding to an ideal Chern band. We validate our proposal by performing numerical simulation of a massive Dirac model, showing that the Berry curvature and quantum metric indeed co-evolve to saturate the trace condition. Our proposal provides a concrete dissipative route to realize ideal Chern bands, a fundamental building block for the stabilization of fractional Chern insulators.