Analytical Bethe ansatz for the open AdS/CFT SU(1|1) spin chain

TL;DR

This paper derives exact eigenvalues and Bethe ansatz equations for the open AdS/CFT SU(1|1) spin chain using an inversion identity and analytic methods, advancing understanding of integrable quantum spin chains.

Contribution

It introduces an exact inversion identity for the open SU(1|1) spin chain and applies it to determine eigenvalues and Bethe ansatz equations, including for the closed chain.

Findings

Derived exact eigenvalues for the open chain

Established Bethe ansatz equations for finite size

Solved the closed chain using algebraic Bethe ansatz

Abstract

We prove an inversion identity for the open AdS/CFT SU(1|1) quantum spin chain which is exact for finite size. We use this identity, together with an analytic ansatz, to determine the eigenvalues of the transfer matrix and the corresponding Bethe ansatz equations. We also solve the closed chain by algebraic Bethe ansatz.