Ground-state properties of the one-dimensional transverse Ising model in a longitudinal magnetic field

TL;DR

This study investigates the phase diagram of the one-dimensional transverse Ising model with a longitudinal magnetic field using quantum fidelity, revealing three phases and challenging previous two-phase assumptions.

Contribution

The paper provides a detailed phase diagram of the 1D transverse Ising model with a longitudinal field, identifying three phases using fidelity susceptibility, which contrasts with earlier two-phase models.

Findings

Identified three distinct phases in the (Bx, Bz)-plane.

Found a disordered phase for Bx > 1 transitioning to paramagnetic.

Contradicted previous literature claiming only two phases.

Abstract

The critical properties of the one-dimensional transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility is used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J2, we calculated the fidelity susceptibility as a function of the transverse field (Bx) and the strength of the longitudinal field (Bz). The phase diagram in the (Bx,Bz)-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For Bx < 1, we observed an antiferromagnetic phase for small values of Bz and a paramagnetic phase for large values of Bz. For Bx > 1 and low Bz, we found a disordered phase that undergoes a phase transition to a paramagnetic phase for large values of Bz.