Hidden dimer order in the quantum compass model

TL;DR

This paper reveals hidden dimer order in the quantum compass model by introducing an exact spin transformation, uncovering correlations that coexist with traditional spin order.

Contribution

An exact spin transformation is developed to map the quantum compass model to simpler models, unveiling hidden dimer correlations in the ground state.

Findings

Unveiled hidden dimer correlations in the quantum compass model.

Mapped the model to smaller quantum spin systems for analysis.

Discovered coexistence of dimer order with Ising-type correlations.

Abstract

We introduce an exact spin transformation that maps frustrated Z_{i,j}Z_{i,j+1} and X_{i,j}X_{i+1,j} spin interactions along the rows and columns of the quantum compass model (QCM) on an LxL square lattice to (L-1)x(L-1) quantum spin models with 2(L-1) classical spins. Using the symmetry properties we unravel the hidden dimer order in the QCM, with equal two-dimer correlations <X_{i,i}X_{i+1,i}X_{k,l}X_{k+1,l}> and <X_{i,i}X_{i+1,i}X_{l,k}X_{l+1,k}> in the ground state, which is independent of the actual interactions. This order coexists with Ising-type spin correlations which decay with distance.