# Scaling of geometric phase versus band structure in cluster-Ising models

## TL;DR

This paper investigates the phase diagram of cluster-Ising models, analyzing how geometric phase scaling relates to band structure topology and quantum phase transitions with different critical exponents.

## Contribution

It introduces a detailed analysis of geometric phase scaling in relation to band topology and characterizes various phases and transitions in cluster-Ising models.

## Key findings

- Identification of phases with local and topological order
- Observation of quantum phase transitions with z=1 and z=2
- Quantification of geometric phase scaling related to band structure

## Abstract

We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary phases with local order parameter or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z = 1 or z = 2 are found. Quantum phase transitions are analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. In particular, we quantify the scaling behavior of the geometric phase in relation with the topology and low energy properties of the band structure of the system.