Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model

TL;DR

This paper demonstrates how infinite Matrix Product States derived from conformal field theories can effectively describe ground states of one-dimensional critical systems with open boundaries, exemplified by the open Haldane-Shastry model.

Contribution

It introduces a novel approach linking conformal field theory-based MPS to open boundary critical systems and derives exact correlations and algebraic structures for the model.

Findings

Exact two-point spin correlation function for the open Haldane-Shastry model

SU(n) generalization of the open Haldane-Shastry model

Identification of twisted Yangian generators responsible for degeneracies

Abstract

We show that infinite Matrix Product States (MPS) constructed from conformal field theories can describe ground states of one-dimensional critical systems with open boundary conditions. To illustrate this, we consider a simple infinite MPS for a spin-1/2 chain and derive an inhomogeneous open Haldane-Shastry model. For the spin-1/2 open Haldane-Shastry model, we derive an exact expression for the two-point spin correlation function. We also provide an SU($n$) generalization of the open Haldane-Shastry model and determine its twisted Yangian generators responsible for the highly degenerate multiplets in the energy spectrum.