Spin-3/2 models on the Cayley tree -- optimum ground state approach

TL;DR

This paper introduces a class of optimal ground states for spin-3/2 models on the Cayley tree, utilizing a generalized matrix product approach to derive exact correlation functions and fluctuations.

Contribution

It develops a new vertex state model for spin-3/2 systems on the Cayley tree, extending the matrix product state method to analyze their ground states.

Findings

Exact analytical expressions for local fluctuations.

Explicit formulas for longitudinal and transversal two-point correlations.

Ground states exhibit parity, spin-flip, and rotational symmetries.

Abstract

We present a class of optimum ground states for spin-3/2 models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions.