Integrable open spin chains related to infinite matrix product states

TL;DR

This paper introduces an integrable open su(m)-invariant spin chain model related to matrix product states, providing explicit conserved charges, spectrum characterization, and statistical properties in the thermodynamic limit.

Contribution

It presents a new integrable open spin chain model linked to matrix product states, with explicit conserved charges and a detailed spectral analysis.

Findings

Model is integrable for roots of Jacobi polynomial

Explicit conserved charges derived from twisted Yangian symmetry

Spectrum described by Haldane's motifs and classical vertex model

Abstract

In this paper we study an su$(m)$-invariant open version of the Haldane-Shastry spin chain whose ground state can be obtained from the chiral correlator of the $c=m-1$ free boson boundary conformal field theory. We show that this model is integrable for a suitable choice of the chain sites depending on the roots of the Jacobi polynomial $P_N^{\beta-1,\beta'-1}$, where $N$ is the number of sites and $\beta,\beta'$ are two positive parameters. We also compute in closed form the first few nontrivial conserved charges arising from the twisted Yangian invariance of the model. We evaluate the chain's partition function, determine the ground state energy and deduce a complete description of the spectrum in terms of Haldane's motifs and a related classical vertex model. In particular, this description entails that the chain's level density is normally distributed in the thermodynamic limit. We also analyze the spectrum's degeneracy, proving that it is much higher than for a typical Yangian-invariant model.