Quantum phase transition and correlations in the multi-spin-boson model

• Published in: Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2014-12, Vol.90 (22), Article 224401
• Main Authors: Winter, André, Rieger, Heiko
• Format: Article
• Language: English
• Subjects: Algorithms; Asymptotic properties; Computer simulation; Condensed matter; Ferromagnetism; Joining; Monte Carlo methods; Phase transformations; Strength
• ISSN: 1098-0121; 1550-235X
• DOI: 10.1103/PhysRevB.90.224401

We consider multiple noninteracting 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 alpha all two-level systems freeze into the same state and the critical value alpha sub(c) 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 arrow right [infinity] 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.