Exact results for a $Z_3$ clock-type model and some close relatives

TL;DR

This paper extends the Peschel-Emery line to a three-state clock model, providing exact ground state solutions, operators transforming these states, and numerical evidence of a gap, with implications for related spin models.

Contribution

It introduces an exactly solvable three-state clock model along a generalized Peschel-Emery line with degenerate ground states and explicit transformation operators.

Findings

Ground states are exactly degenerate and can be written as product states.

The model is numerically shown to be gapped.

Exact excited states are identified for these models.

Abstract

In this paper, we generalized the Peschel-Emery line of the interacting transverse field Ising model to a model based on three-state clock variables. Along this line, the model has exactly degenerate ground states, which can be written as product states. In addition, we present operators that transform these ground states into each other. Such operators are also presented for the Peschel-Emery case. We numerically show that the generalized model is gapped. Furthermore, we study the spin-S generalization of interacting Ising model and show that along a Peschel-Emery line they also have degenerate ground states. We discuss some examples of excited states that can be obtained exactly for all these models.