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.
Highlights
The process in which a quantum system undergoes decoherence due to its environment is generally termed “dissipation”
It has become clear that an array of two-level systems coupled to a dissipative reservoir exhibits phenomena beyond those described by the spin boson model
Ultra cold atoms in an optical lattice can form two-level systems immersed in a Bose-Einstein condensate (BEC), where the Goldstone modes of the superfluid produce a shared bosonic bath
Summary
The process in which a quantum system undergoes decoherence due to its environment is generally termed “dissipation”. Ohmic dissipation is a natural choice because it is realized in the BEC-embedded optical lattice implementation.[7] The dimensionless constant α determines the strength of the dissipation and in the case of a single spin controls the phase transition between a quantum paramagnetic phase and the decoherent “localized” phase.[8,9] We have introduced the frequency cutoff function fωc (ω), which is often chosen to be in the form of either a hard cutoff fωc (ω) = Θ(ωc − ω) or a smooth exponential cutoff fωc (ω) = exp(−ω/ωc). Q is the bosonic analog of the Fermi momentum in the conventional RKKY interaction In this Contribution, we study the model defined in Eq (1) with classical Monte Carlo simulations via a quantum-to-classical mapping. We conclude by suggesting the region(s) of the phase diagram that can be studied by the methods outlined in this Contribution
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