Quantum Monte Carlo simulation of spin-boson models using wormhole updates

Abstract

We present an exact quantum Monte Carlo method for spin systems coupled to dissipative bosonic baths which makes use of nonlocal wormhole updates to simulate the retarded spin-flip interactions originating from an off-diagonal spin-boson coupling. The method is closely related to the stochastic series expansion and extends the scope of the global directed-loop updates to nonlocal moves through a world-line configuration. We test our method for the U(1)-symmetric two-bath spin-boson model, where the off-diagonal components of a spin-$1/2$ particle are coupled to identical independent baths with power-law spectra, and get a precise estimate of the critical coupling between the critical and the localized phase. Our method applies to impurity systems and lattice models in any spatial dimension coupled to bosonic modes with arbitrary spectral distributions.

15 pages, 5 figures; final version

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• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality
• Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
• Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• The light-matter correlation energy functional of the cavity-coupled two-dimensional electron gas via quantum Monte Carlo simulations
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model