Noise-driven quantum criticality

TL;DR

This paper introduces a framework for defining and analyzing quantum critical exponents in open quantum systems driven by noise, revealing scaling laws and critical behavior in steady states of dissipative lattice models.

Contribution

It develops a complete description of steady states in noisy free bosonic and fermionic systems, enabling the calculation of correlation properties and critical exponents.

Findings

Steady states exhibit scaling laws for correlation length divergence.

Critical exponents are characterized for bosonic and fermionic models.

The approach parallels Fisher-Hartwig theory for free models.

Abstract

We discuss a notion of quantum critical exponents in open quantum many-body systems driven by quantum noise. We show that in translationally invariant quantum lattice models undergoing quasi-local Markovian dissipative processes, mixed states emerge as stationary points that show scaling laws for the divergence of correlation lengths giving rise to well-defined critical exponents. The main new technical tool developed here is a complete description of steady states of free bosonic or fermionic translationally invariant systems driven by quantum noise: This approach allows to express all correlation properties in terms of a symbol, paralleling the Fisher-Hartwig theory used for ground state properties of free models. We discuss critical exponents arising in bosonic and fermionic models. Finally, we relate the findings to recent work on dissipative preparation of pure dark and matrix product states by Markovian noisy processes and sketch further perspectives.