Level Statistics of Multispin-Coupling Models with First and Second Order Phase Transitions

TL;DR

This paper analyzes the spectral properties of multispin-coupling Ising models with different order phase transitions, revealing universal level statistics behaviors and symmetry effects near critical points.

Contribution

It provides a detailed statistical analysis of the energy spectra of self-dual transverse-field Ising chains with multispin interactions, highlighting the effects of phase transition order and symmetries.

Findings

Level repulsion near Wigner distribution outside critical points

Superposition of two Wigner distributions at the transition due to symmetry

No evidence of integrability for m>2 even at transition

Abstract

We consider self-dual transverse-field Ising spin chains with $m$-spin interaction, where the phase transition is of second and first order, for m <= 3 and m>3, respectively. We present a statistical analysis of the spectra of the Hamiltonians on relatively large L <= 18 finite lattices. Outside the critical point we found level repulsion close to the Wigner distribution and the same rigidity as for the Gaussian Orthogonal Ensemble. At the transition point the level statistics in the self-dual sector is shown to be the superposition of two independent Wigner distributions. This is explained by the existence of an extra symmetry, which is connected to level crossing in the thermodynamic limit. Our study has given no evidence for the possible integrability of the models for m>2, even at the transition point.