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 $\nu$ 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 $z\approx 1$.

9 pages, 8 figures. Submitted to Physical Review B

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