Monte-Carlo simulations of the dissipative random transverse-field Ising chain

TL;DR

This paper uses large-scale Monte-Carlo simulations to investigate how Ohmic dissipation affects the quantum phase transition in the random transverse-field Ising chain, revealing that dissipation smears the transition instead of preserving the critical point.

Contribution

It introduces a Monte-Carlo simulation approach with a long-range interaction mapping to study dissipation effects on the quantum critical behavior of the Ising chain, providing new insights into phase transition smearing.

Findings

Ohmic dissipation destroys the infinite-randomness quantum critical point.

The quantum phase transition becomes smeared due to dissipation.

Simulation results align with strong-disorder renormalization group predictions.

Abstract

We study the influence of Ohmic dissipation on the random transverse-field Ising chain by means of large-scale Monte-Carlo simulations. To this end, we first map the Hamiltonian onto a classical Ising model with long-range $1/\tau^2$ interaction in the time-like direction. We then apply the highly efficient cluster algorithm proposed by Luijten and Bl\"ote for system with long-range interactions. Our simulations show that Ohmic dissipation destroys the infinite-randomness quantum critical point of the dissipationless system. Instead, the quantum phase transition between the paramagnetic and ferromagnetic phases is smeared. We compare our results to recent predictions of a strong-disorder renormalization group approach, and we discuss generalizations to higher dimensions as well as experiments.