Quantum spherical spin models

TL;DR

This paper analyzes exactly solvable quantum spherical spin models with different symmetry classes, revealing how the presence or absence of momenta in the Hamiltonian affects their phase diagrams and critical phenomena.

Contribution

It introduces and compares two quantum spherical spin models with distinct symmetry properties, providing exact solutions and phase diagrams.

Findings

Models exhibit different critical behaviors depending on symmetry class.

Phase transition lines end in quantum critical points.

Model with momenta resembles SU(N) ferromagnet behavior.

Abstract

A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without momenta in the Hamiltonian can be described, which may lead to different symmetry classes. Two models that show this difference are analyzed. Both models are exactly solvable and their phase diagram is analyzed. A transversal external field leads to a phase transition line that ends in a quantum critical point. The two considered symmetries of the Hamiltonian considered give different critical phenomena in the quantum critical region. The model with momenta is argued to be analog to the large-N limit of an SU(N) Heisenberg ferromagnet, and the model without momenta shares the critical phenomena of an SU(N) Heisenberg antiferromagnet.