Crosscap States in Integrable Spin Chains

Sammanfattning: We consider integrable boundary states in the Heisenberg model. We begin by reviewing the algebraic Bethe Ansatz as well as integrable boundary states in spin chains. Then a new class of integrable states that was introduced last year by Caetano and Komatsu is described and expanded. We call these states the crosscap states. In these states each spin is entangled with its antipodal spin. We present a novel proof of the integrability of both a crosscap state that is known in the literature and one that is not previously known. We then use the machinery of the algebraic Bethe Ansatz to derive the overlaps between the crosscap states and off-shell Bethe states in terms of scalar products and other known overlaps.