Integrable open spin chains related to infinite matrix product states

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 $P_N^{\beta -1,{\beta }^{\prime }-1}$, where $N$ is the number of sites and $\beta ,{\beta }^{\prime }$ 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.

RevTeX, 11 pages (enlarged version, to appear in Phys. Rev. B)

References in corpus (6)

• Dynamical crystallization in a low-dimensional Rydberg gas
• Quantum critical behavior in strongly interacting Rydberg gases
• Infinite Matrix Product States for long range SU(N) spin models
• Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Yangian-invariant spin models and Fibonacci numbers

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