Quantum phase transition in the spin-anisotropic quantum spherical model

Abstract

Motivated by an analogy with the spin anisotropies in the quantum XY chain and its reformulation in terms of spin-less Majorana fermions, its bosonic analogue, the spin-anisotropic quantum spherical model, is introduced. The exact solution of the model permits to analyse the influence of the spin-anisotropy on the phase diagram and the universality of the critical behaviour in a new way, since the interactions of the quantum spins and their conjugate momenta create new effects. At zero temperature, a quantum critical line is found, which is in the same universality class as the thermal phase transition in the classical spherical model in $d+1$ dimensions. The location of this quantum critical line shows a re-entrant quantum phase transition for dimensions $1<d\lesssim 2.065$.

34 pages, Latex2e, 3 figures, final form

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Cited by in corpus (20)

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• Axiomatic construction of quantum Langevin equations
• Dynamical chaotic phases and constrained quantum dynamics
• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field $XY$ model
• Entanglement gap, corners, and symmetry breaking
• Quantum dynamics far from equilibrium: a case study in the spherical model
• Entanglement in the Quantum Spherical Model -- a Review
• Limitations of the Markovian approximation in the harmonic oscillator
• Entanglement gap in 1D long-range quantum spherical models
• Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality
• Two-dimensional easy-plane SU$(3)$ magnet with the transverse field: Anisotropy-driven multicriticality
• Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results
• Supersymmetric Quantum Spherical Spins
• Spherical model with Dzyaloshinskii-Moriya interactions
• Supersymmetric Quantum Spherical Spins with Short-Range Interactions