Dissipative free fermions in disguise

TL;DR

This paper extends the concept of free fermions in disguise to open quantum systems, identifying conditions under which their Liouvillian spectra are exactly solvable and revealing new insights into their spectral properties.

Contribution

It introduces a framework for exactly solvable open quantum systems within the FFD class, based on graph-theoretic conditions of the Liouvillian.

Findings

Liouvillian spectra can be exactly computed under certain graph conditions.

The FFD mechanism is realized in open quantum systems for the first time.

Exact solutions enable analysis of Liouvillian gap and autocorrelation functions.

Abstract

Recently, a class of spin chains known as ``free fermions in disguise'' (FFD) has been discovered, which possess hidden free-fermion spectra even though they are not solvable via the standard Jordan-Wigner transformation. In this work, we extend this FFD framework to open quantum systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We establish a general class of exactly solvable open quantum systems within the FFD framework: if the Liouvillian frustration graph is claw-free and has a simplicial clique, the Liouvillian possesses a hidden free-fermion spectrum. In particular, the (even-hole, claw)-free condition automatically guarantees this, enabling exact computation of the Liouvillian gap and an infinite-temperature autocorrelation function. Our results provide the first realization of the FFD mechanism in open quantum systems.