The quantum phase transition and correlations in the multi-spin-boson model

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We consider multiple non-interacting quantum mechanical two-level systems coupled to a common bosonic bath and study its quantum phase transition with Monte Carlo simulations using a continuous imaginary time cluster algorithm. The common bath induces an effective ferromagnetic interaction between the otherwise independent two-level systems, which can be quantified by an effective interaction strength. For degenerate energy levels above a critical value of the bath coupling strength α all two-level systems freeze into the same state and the critical value αc decreases asymptotically as 1/N with increasing N. For a finite number, N, of two-level systems the quantum phase transition (at zero temperature) is in the same universality class as the single spin-boson model, in the limit N→∞ the system shows mean-field critical behavior independent of the power of the spectral function of the bosonic bath. We also study the influence of a spatial separation of the spins in a bath of bosonic modes with linear dispersion relation on the location and characteristics of the phase transition as well as on correlations between the two-level systems.