Entanglement and correlation functions of a recent exactly solvable spin chain

Ramis Movassagh

Published Feb 25, 2016• 2 citations

Abstract

standard spin-basis representation. We prove that at zero temperature, the magnetization is along the z direction i.e.,hs x i = hs y i = 0 (everywhere on the chain). We then analytically calculatehs z i and the two-point correlation functions of s z . By analytically diagonalizing the reduced density matrices, we calculate the Schmidt rank, von Neumann and Renyi entanglement entropies for: 1. Any partition of the chain into two pieces (not necessarily in the middle) and 2. L consecutive spins centered in the middle. Further, we identify entanglement Hamiltonians (Eqs. 40 and 50). We prove a small lemma (Lemma 1) on the combinatorics of lattice paths using the reflection principle to relate and calculate the Motzkin walk ’height’ to spin expected values. We also calculate the, closely related, (scaled) correlation functions of Brownian excursions. The known features of this model are summarized in a table in Sec. I.

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