TL;DR
This paper introduces a method to compute the Berry phase in lattice QCD by projecting the ground state of a fermion and calculating the Berry link variable, demonstrated through the first Chern number of (2+1)D Wilson fermions.
Contribution
It presents a novel lattice QCD approach to calculate the Berry phase and demonstrates its application to topological invariants like the Chern number.
Findings
Successfully calculated the first Chern number of (2+1)D Wilson fermions.
Established a new method for Berry phase computation in lattice QCD.
Demonstrated the feasibility of Monte Carlo simulation for topological quantities.
Abstract
We propose the lattice QCD calculation of the Berry phase which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.
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