Hidden dimer order in the quantum compass model

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 $L\ifmmode\times\else\texttimes\fi{}L$ square lattice to $(L\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}(L\ensuremath{-}1)$ quantum spin models with $2(L\ensuremath{-}1)$ 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.