Corner space renormalization method for driven-dissipative 2D correlated systems

TL;DR

This paper introduces a corner space renormalization method to efficiently compute the steady states of driven-dissipative 2D correlated lattice systems, demonstrated on the Bose-Hubbard model.

Contribution

A novel iterative corner space approach for solving the master equation in 2D driven-dissipative systems, improving accuracy by increasing the number of states.

Findings

Efficiently computes steady states of 2D driven-dissipative systems.

Demonstrates accuracy and convergence on the 2D Bose-Hubbard model.

Applicable to complex quantum optical lattice systems.

Abstract

We present a theoretical method to study driven-dissipative correlated systems on lattices with two spatial dimensions (2D). The steady-state density-matrix of the lattice is obtained by solving the master equation in a corner of the Hilbert space. The states spanning the corner space are determined through an iterative procedure, using eigenvectors of the density-matrix of smaller lattice systems, merging in real space two lattices at each iteration and selecting M pairs of states by maximizing their joint probability. Accuracy of the results is then improved by increasing M, the number of states of the corner space, until convergence is reached. We demonstrate the efficiency of such an approach by applying it to the driven-dissipative 2D Bose-Hubbard model, describing, e.g., lattices of coupled cavities with quantum optical nonlinearities.