The gap exponent of XXZ model in a transverse field

TL;DR

This paper numerically investigates the gap exponent of the XXZ model under a transverse magnetic field, revealing how the energy gap scales with anisotropy and diverges in the thermodynamic limit, aligning with field theory predictions.

Contribution

The study introduces a numerical method to accurately compute the excited states of the XXZ model and establishes the relation between divergence of perturbation coefficients and energy gap scaling.

Findings

Gap opens with a critical exponent depending on anisotropy.

Numerical results agree with field theoretical predictions.

Divergence of perturbation coefficient relates to gap scaling.

Abstract

We have calculated numerically the gap exponent of the anisotropic Heisenberg model in the presence of the transverse magnetic field. We have implemented the modified Lanczos method to obtain the excited states of our model with the same accuracy of the ground state. The coefficient of the leading term in the perturbation expansion diverges in the thermodynamic limit (N --> infinity). We have obtained the relation between this divergence and the scaling behaviour of the energy gap. We have found that the opening of gap in the presence of transverse field scales with a critical exponent which depends on the anisotropy parameter (Delta). Our numerical results are in well agreement with the field theoretical approach in the whole range of the anisotropy parameter, -1 < Delta < 1.