Matrix Product State and Quantum Phase Transitions in the One-Dimensional Extended Quantum Compass Model

TL;DR

This paper uses matrix product states to analyze ground states and quantum phase transitions in the one-dimensional extended quantum compass model, revealing how entanglement and correlation measures detect different types of phase transitions.

Contribution

It demonstrates the effectiveness of MPS in studying QCM ground states and identifies specific entanglement features associated with quantum phase transitions.

Findings

Bipartite and block entanglement entropies detect second-order QPTs.

Fidelity can recognize both first- and second-order QPTs.

Entanglement spectrum is doubly degenerate in disordered phases.

Abstract

The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of QCM ground states, and are numerically determined by imaginary time projections. The ground state energy, correlations, quantum entanglement and its spectrum, local and nonlocal order parameters, etc., are calculated and studied in details. It is revealed that the bipartite and block entanglement entropies, as well as the nearest neighbor correlation functions can be used to detect the second-order QPTs, but not the first-order ones, while fidelity detections can recognize both. The entanglement spectrum is extracted from the MPS wavefunction, and found to be doubly degenerate in disordered phases of QCM, where non-local string order parameters exist. Moreover, with linearized tensor renormalization group method, the specific heat curves are evaluated and their low temperature behaviors are investigated.