Symmetry-protected trivial phases and quantum phase transitions in an anisotropic antiferromagnetic spin-1 biquadratic model

TL;DR

This paper maps out the phase diagram of an anisotropic spin-1 biquadratic model, revealing symmetry-protected trivial phases, their quantum transitions, and unique factorized ground states.

Contribution

It identifies new symmetry-protected trivial phases and their quantum phase transitions, with detailed characterization using order parameters and universality classes.

Findings

Three symmetry-protected trivial phases identified

Quantum phase transitions belong to Gaussian and Ising classes

Existence of three factorized ground state lines within trivial phases

Abstract

The ground state phase diagram is obtained for an antiferromagnetic spin-1 anisotropic biquadratic model. With the help of symmetry and duality transformations, three symmetry-protected trivial phases and one dimerized symmetry breaking phase are found. Local and nonlocal order parameters are identified to characterize these phases. Quantum phase transitions between the symmetry-protected trivial phases belong to the Gaussian universality class with central charge c = 1, and quantum phase transitions from the symmetry-protected trivial phases to the dimerized phase belong to the Ising universality class with central charge c = 1/2. In addition, the model admits three characteristic lines of factorized ground states, which are located in the symmetry-protected trivial phases instead of a symmetry breaking phase, in sharp contrast to other known cases.