Phase transitions and thermal entanglement of the distorted Ising-Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

TL;DR

This paper analyzes a complex spin ladder model with multiple interactions, revealing rich phase diagrams, quantum phase transitions, and how heat capacity and entanglement are affected by cyclic four-spin exchange interactions.

Contribution

It provides an exact solution for a distorted Ising-Heisenberg spin ladder with multiple interactions, highlighting the sensitivity of heat capacity and entanglement to cyclic four-spin exchange.

Findings

Heat capacity is sensitive to cyclic four-spin exchange interactions.

A singularity relation links cyclic four-spin exchange and rung exchange coupling.

Thermal entanglement is characterized by concurrence in the thermodynamic limit.

Abstract

We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We here prove that among the considered thermodynamic and thermal parameters, solely the heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should investigate by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.