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

O. F. de Alcantara Bonfim, B. Boechat, and J. Florencio
Phys. Rev. E 99, 012122 – Published 14 January 2019

Abstract

The critical properties of the one-dimensional spin-1/2 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 was 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 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 second-order phase transition to a paramagnetic phase for large values of Bz.

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  • Received 22 August 2018
  • Revised 23 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.012122

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

O. F. de Alcantara Bonfim*

  • Department of Physics, University of Portland, Portland, Oregon 97203, USA

B. Boechat and J. Florencio

  • Departamento de Física, Universidade Federal Fluminense Av. Litorânea s/n, Niterói, 24210-340, RJ, Brazil

  • *bonfim@up.edu
  • bmbp@if.uff.br
  • jfj@if.uff.br

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Vol. 99, Iss. 1 — January 2019

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