Exact solution for a quantum compass ladder

TL;DR

This paper presents an exact solution for a quantum compass ladder model, revealing its energy spectrum, phase transition behavior, and thermodynamic properties, thereby enhancing understanding of quantum phase transitions in frustrated spin systems.

Contribution

It introduces an exact analytical approach to solve the quantum compass ladder, connecting it to the quantum Ising model and analyzing phase transitions and thermodynamics.

Findings

Exact energy spectrum determined via Jordan-Wigner transformation.

Collapse of rung spin correlations at the quantum phase transition.

Heat capacity shows two energy scales and broad maximum.

Abstract

We introduce a spin ladder with antiferromagnetic Ising ZZ interactions along the legs, and interactions on the rungs which interpolate between the Ising ladder and the quantum compass ladder. We show that the entire energy spectrum of the ladder may be determined exactly for finite number of spins 2N by mapping to the quantum Ising chain and using Jordan-Wigner transformation in invariant subspaces. We also demonstrate that subspaces with spin defects lead to excited states using finite size scaling, and the ground state corresponds to the quantum Ising model without defects. At the quantum phase transition to maximally frustrated interactions of the compass ladder, the ZZ spin correlation function on the rungs collapses to zero and the ground state degeneracy increases by 2. We formulate a systematic method to calculate the partition function for a mesoscopic system, and employ it to demonstrate that fragmentation of the compass ladder by kink defects increases with increasing temperature. The obtained heat capacity of a large compass ladder consisting of 2N=104 spins reveals two relevant energy scales and has a broad maximum due to dense energy spectrum. The present exact results elucidate the nature of the quantum phase transition from ordered to disordered ground state found in the compass model in two dimensions.