Geometric Phase in Kitaev Quantum Spin Liquid

TL;DR

This paper introduces the concept of sub-geometric phase in the density matrix to characterize topological properties of the Kitaev quantum spin liquid, revealing its effects on physical observables and state stability.

Contribution

It extends geometric phase concepts to the density matrix, enabling the study of topological features in quantum spin liquids through observable physical quantities.

Findings

Imaginary part of sub-geometric phase affects resonance peaks and energy level crossing.

Real part of sub-geometric phase influences the stability of quantum states.

Sub-geometric phase provides insights into quantum transition rules.

Abstract

Quantum spin liquid has massive many spin entanglement in the ground state, we can evaluate it by the entanglement entropy, but the latter can not be observed directly by experiment. In this manuscript, we try to characterize its topological properties by the geometric phase. However the usual adiabatic or non-adiabatic geometric phase can not appear in the density matrix of entanglement entropy, so we extend it to the sub-geometric phase which can exist in the density matrix and have influence on the entanglement entropy, spin correlation function as well as other physical observable. We will demonstrate that the imaginary part of sub-geometric phase will deviate the resonance peak by an amount concerning with this phase and affect the energy level crossing, while the real part of sub-geometric phase will determine the stability of initial state, it may provide a complement on the selection rule of quantum transition.