Quantum phase transition of the one-dimensional compass model in a transverse magnetic field

TL;DR

This paper investigates the quantum phase transition in a 1D quantum compass model under a transverse magnetic field, revealing a second-order transition at zero field with critical behavior similar to the 1D Ising model.

Contribution

The study provides an exact solution for the 1D quantum compass model in a transverse field and analyzes its critical properties, including entanglement and correlation functions, highlighting its universality class.

Findings

Quantum phase transition occurs only at zero transverse field.

Critical exponents match those of the 1D transverse field Ising model.

Entanglement entropy diverges logarithmically at the critical point.

Abstract

The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudo-spin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudo-spin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse field only emerges at zero field and is of the second-order. Several critical exponents obtained by finite size scaling analysis are the same as those in the 1D transverse field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.