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

Abstract

Environmental interaction is a fundamental consideration in any controlled quantum system. While interaction with a dissipative bath can lead to decoherence, it can also provide desirable emergent effects including induced spin-spin correlations. In this paper we show that under quite general conditions, a dissipative bosonic bath can induce a long-range ordered phase, without the inclusion of any additional direct spin-spin couplings. Through a quantum-to-classical mapping and classical Monte Carlo simulation, we investigate the T = 0 quantum phase transition of an Ising chain embedded in a bosonic bath with Ohmic dissipation. We show that the quantum critical point is continuous, Lorentz invariant with a dynamical critical exponent z = 1.07(9), has correlation length exponent ν = 0.80(5), and anomalous exponent η = 1.02(6), thus the universality class distinct from the previously studied limiting cases. The implications of our results on experiments in ultracold atomic mixtures and qubit chains in dissipative environements are discussed.