Quantum phase transitions in matrix product systems

TL;DR

This paper explores quantum phase transitions in spin chain systems with matrix product ground states, revealing unique transition characteristics such as finite entanglement entropy and analytic ground state energy, differing from traditional QPTs.

Contribution

It introduces a method to engineer quantum phase transitions with specific properties in matrix product systems, expanding understanding of non-standard QPT behavior.

Findings

Transitions can occur with finite entanglement entropy.

Ground state energy remains analytic across transitions.

Transitions can occur at triple points of conventional QPTs.

Abstract

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of `conventional' QPTs.