Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field

TL;DR

This paper investigates the quantum critical behavior and excitations of a long-range anisotropic XY chain in a transverse field, combining analytical, numerical, and perturbative methods to understand phase breakdown and critical exponents.

Contribution

It introduces a comprehensive approach using series expansions, Monte Carlo simulations, and quantum field theory to analyze quantum criticality in long-range anisotropic XY models.

Findings

Determined the elementary quasi-particle dispersion analytically for the isotropic case.

Calculated two quasi-particle excitation energies numerically.

Extracted critical exponents and analyzed gap-closing behavior at quantum phase transitions.

Abstract

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferro- and antiferromagnetic case. While for the limiting case of the isotropic long-range XY model we can extract the elementary one quasi-particle dispersion analytically and calculate two quasi-particle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap-closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents $z$ and $\nu$ analytically by a bosonic quantum-field theory.