Efficient Monte Carlo simulation of a dissipative Ising chain

Abstract

We numerically study the dissipative transverse field Ising model in a bosonic bath with Ohmic spectral density. We present Monte Carlo techniques for studying this model in previously inaccessible regimes of strong frustration. We then consider a well-studied limit of this model, infinite-separation, and further show that even for finite separations there is no magnetic ordering associated with the case of an infinite bath cutoff frequency. We discuss future applications for the Monte Carlo method.

Long-Range Order and Quantum Criticality in a Dissipative Spin Chain

“…Intriguingly, we find that the quantum critical exponents found here for finite λ characterize a novel universality class, fundamentally distinct from the previously studied limits of λ → ∞ (i.e. ω c → 0) [31] and the limit of λ → 0, which corresponds to each spin in a chain coupled to an independent bath [44]. In either of these two asymptotic cases, the quantum critical properties reduce to a BKT transition of the single spin model in a bosonic bath [7][8][9].…”

“…In the opposite limit (ii) λ → 0, the spins are completely decoupled from one another and the DTFIM maps onto a model where each spin couples to an independent bath. This model has been studied previously, including by the present authors [29,44]. In this work, we explore the most nontrivial case of finite λ ∼ 1, and show that the resulting QCP has distinct critical exponents from the aforementioned limiting cases.…”

“…By integrating out the bosons and performing a quantum-to-classical mapping [43], we arrive at the partition function of a 1+1-dimensional classical Ising model [44]:…”

“…The longrange interactions include frustration, which causes an exponential slowdown of autocorrelation times in naïve Monte Carlo simulations [47]. In order to counteract this effect, the simulations were performed with a combination of Metropolis updates, modified Wolff cluster updates, and parallel tempering updates [44]. The procedure for cluster updates is based on the Luijten-Blöte modified Wolff algorithm for long-range interactions [48], however the presence of mixed-sign interactions (see Fig.…”

“…The procedure for cluster updates is based on the Luijten-Blöte modified Wolff algorithm for long-range interactions [48], however the presence of mixed-sign interactions (see Fig. 1b) necessitates a modification where the acceptance probability for adding a given spin to the cluster is calculated from the absolute value of the interaction strength [44,49,50]. In addition to the cluster updates, parallel tempering [51] in the dissipation strength α is employed.…”