# Solvable Markovian dynamics of lattice quantum spin models

## TL;DR

This paper presents an exact method for analyzing the real-time dynamics of lattice quantum spin models with Markovian dissipation, enabling the study of large systems and their steady states.

## Contribution

The authors develop a closed hierarchy approach that allows exact solutions of quantum spin models in arbitrary dimensions with dissipation.

## Key findings

- Exact solutions for driven-dissipative quantum spin models.
- Analytical derivation of characteristic time scales and finite-size scaling.
- Numerical confirmation of dissipative gap scaling exponents.

## Abstract

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.