Monte Carlo simulations of dissipative quantum Ising models

TL;DR

This paper uses Monte Carlo simulations to study how different types of dissipation affect the dynamical critical exponent in quantum Ising models, revealing that dissipation type influences critical behavior.

Contribution

It provides the first estimates of the dynamical critical exponent $z$ for 1D and 2D dissipative quantum Ising models with different dissipation forms using Monte Carlo methods.

Findings

For 2D quantum Ising with Ohmic site dissipation, z ≈ 2.

For 1D quantum Ising with Ohmic bond dissipation, z ≈ 1.

Dissipation type significantly affects the critical exponent.

Abstract

The dynamical critical exponent $z$ is a fundamental quantity in characterizing quantum criticality, and it is well known that the presence of dissipation in a quantum model has significant impact on the value of $z$. Studying quantum Ising spin models using Monte Carlo methods, we estimate the dynamical critical exponent $z$ and the correlation length exponent $\nu$ for different forms of dissipation. For a two-dimensional quantum Ising model with Ohmic site dissipation, we find $z \approx 2$ as for the corresponding one-dimensional case, whereas for a one-dimensional quantum Ising model with Ohmic bond dissipation we obtain the estimate $z \approx 1$.