Quantum renormalization group approach to geometric phases in spin chains

TL;DR

This paper investigates the relationship between geometric phases and quantum criticality in spin chains using a quantum renormalization-group approach, revealing how geometric phases behave near critical points and their finite size scaling.

Contribution

It introduces a quantum renormalization-group method to analyze geometric phases in spin chains and connects their divergence to critical properties and correlation length exponents.

Findings

The geometric phase's first derivative diverges at the critical point.

Finite size scaling of the geometric phase's derivative reveals critical exponents.

The critical exponent matches the correlation length divergence exponent.

Abstract

A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative and its position scales with an exponent of the system size. This exponent is directly associated with the critical properties of the model where, the exponent governing the divergence of the correlation length close to the quantum critical point.