Monte Carlo simulations of dissipative quantum Ising models

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 $\ensuremath{\nu}$ for different forms of dissipation. For a two-dimensional quantum Ising model with Ohmic site dissipation, we find $z\ensuremath{\approx}2$ as for the corresponding one-dimensional case, whereas for a one-dimensional quantum Ising model with Ohmic bond dissipation, we obtain the estimate $z\ensuremath{\approx}1$.