Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2

TL;DR

This paper introduces an infinite family of exactly solvable spin chains, revealing their phase transitions belong to universality classes with central charge c=m/2, and provides a unified framework connecting XY and cluster states.

Contribution

It develops a novel method to diagonalize these models, extending solvability beyond traditional transformations like Jordan-Wigner, and uncovers a unified structure linking XY and cluster-type chains.

Findings

Ground-state phase transitions have central charge c=m/2.

Models include stabilizers of the cluster state.

Derived phase diagram and correlation functions.

Abstract

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c=m/2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.