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arXiv:1303.3281

Geometric Phase and Fidelity of The One-Dimensional Extended Quantum Compass Model in a Transverse Field

Rouhollah Jafari

Published Mar 13, 2013• 0 citations
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Abstract

We study the geometric phase of the ground state in the extended quantum compass model in presence of a transverse field. The exact solution is obtained by using the Jordan-Wigner transformation which maps the Hamiltonian on a fermionic system and applying the Fourier transformation to realize the diagonalization and an analytical expression for the ground state and geometric phase in the momentum space. Furthermore, the scaling behavior of the extremum of geometric phase and its universality are investigated due to the divergence of geometric phase at the critical point.

DOI
10.48550/arxiv.1303.3281

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We present an exact solution for a class of one-dimensional compass models which stand for interacting orbital degrees of freedom in a Mott insulator. By employing the Jordan-Wigner transformation we map these models on noninteracting fermions and discuss how spin correlations, high degeneracy of the ground state, and Z2{Z}_{2}Z2​ symmetry in the quantum compass model are visible in the fermionic language. Considering a zigzag chain of ions with singly occupied eg{e}_{g}eg​ orbitals (eg{e}_{g}eg​ orbital model) we demonstrate that the orbital excitations change qualitatively with increasing transverse field, and that the excitation gap closes at the quantum phase transition to a polarized state. This phase transition disappears in the quantum compass model with maximally frustrated orbital interactions which resembles the Kitaev model. Here we find that the finite transverse field destabilizes the orbital-liquid ground state with macroscopic degeneracy, and leads to peculiar behavior of the specific heat and orbital susceptibility at finite temperature. We show that the entropy and the cooling rate at finite temperature exhibit quite different behavior near the critical point for these two models.