Linked cluster expansions for open quantum systems on a lattice

TL;DR

This paper introduces a generalized linked-cluster expansion method for open quantum lattice systems, enabling analysis of phase transitions and critical behavior directly in the thermodynamic limit.

Contribution

It extends linked-cluster expansions to driven-dissipative quantum systems, allowing for efficient study of phase transitions in large lattice models.

Findings

Successfully applied to spin-1/2 models with dissipation

Able to locate phase transition points using series analysis

Provided estimates for critical exponents of susceptibility

Abstract

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Pad\'e analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.