Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach

TL;DR

This paper constructs and analyzes a family of quantum ground states for spin-3/2 systems on a hexagonal lattice, revealing a parameter-driven second order phase transition with distinct correlation behaviors.

Contribution

It introduces a novel vertex state model approach for two-dimensional spin systems and identifies a phase transition not present in one-dimensional analogs.

Findings

Existence of a one-parameter set of ground states for S=3/2 Hamiltonians.

Identification of a second order phase transition driven by the parameter.

Correlation functions show exponential decay in disordered phase and long-range order in the ordered phase.

Abstract

Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a one-parametric set of ground states for a five-dimensional manifold of S=3/2 Hamiltonians. Correlation functions within these ground states are calculated using Monte-Carlo simulations. In contrast to the one-dimensional situation, these states exhibit a parameter-induced second order phase transition. In the disordered phase, two-spin correlations decay exponentially, but in the Neel ordered phase alternating long-range correlations are dominant. We also show that ground state properties can be obtained from the exact solution of a corresponding free-fermion model for most values of the parameter.