Bargmann Representation of Spin Chains

TL;DR

This paper presents a representation of spin chain Hamiltonians using the Bargmann framework, expressing eigenfunctions as monomials in complex phase-space coordinates, facilitating classical limit analysis and quasi-probability calculations.

Contribution

It introduces a novel Bargmann representation for spin chains, linking complex differential operators with eigenfunctions expressed as monomials in phase-space coordinates.

Findings

Eigenfunctions are expressed as products of orthonormal monomials.

Series in phase-space coordinates converge uniformly in compact domains.

The approach aids in analyzing classical limits and quasi-probability distributions.

Abstract

Spin chain Hamiltonians can be written in terms of complex differential operators using the Bargmann representation of the Jordan-Schwinger map. In this case, the eigenfunctions are expressed as the product of orthonormal monomials of the phase-space coordinates $z_{i}=Q_{i}+i P_{i}$ in the complex plane. Furthermore, the series constructed from each phase-space coordinate converges uniformly in any compact domain of the complex plane. Formulating spin chains with respect to the phase-space coordinates helps in discussing their classical limit and in the calculations of quasi-probability distributions.