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, where N is the number of sites and β, β ′ 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.

Exactly Solvable Quantum Impurity Model with Inverse-Square Interactions

“…If the vertex operators for the impurity site were removed from Eq. (9), the wave function reduces to the ground state of H 0 that realizes the free-fermion CFT with the free boundary condition on the lattice [63][64][65][66]. This is perhaps not too surprising, since the vertex operators (10) for conduction fermions all have conformal weight h = 1/2 and thus are fermionic fields.…”

A novel class of translationally invariant spin chains with long-range interactions

“…It is also apparent from these plots that the degeneracy of the new chain grows exponentially with N , as is typically the case for Yangian-invariant models [71]. All of these facts strongly suggest that the model (2.1) possesses some kind of (twisted) Yangian symmetry not only in the even m case, as shown in the previous section, but also for odd m. This is typically the case for similar open chains with long-range interactions like the BC N , B N and D N HS chains or the Simons-Altshuler model [40,44,74] and its integrable generalizations [45].…”

“…More recently, exact ground state wavefunctions of some HS-like spin chains, with open boundary conditions and lattice points arbitrarily distributed on a half-circle, have been constructed using infinite MPSs related to suitable boundary CFTs and corresponding null fields [44]. Again, these CFT-inspired generalizations of the HS chain with open boundary conditions become integrable [44] and, in fact, exactly solvable [45], only for some special choices of the lattice points, but none of them possess the translational invariance of the original HS chain.…”

A novel class of translationally invariant spin chains with long-range interactions

“…All of these facts strongly suggest that the model (2.1) possesses some kind of Yangian symmetry, as is known to be the case for the original (A N −1 ) HS chain [2]. In fact, given the open character of the new model it is more likely that its underlying symmetry group is a twisted Yangian, as is the case for similar open chains with long-range interactions like the BC N , B N and D N HS chains or the Simons-Altshuler model [40,44,65] and its integrable generalizations [45].…”

“…More recently, exact ground state wavefunctions of some HSlike spin chains, with open boundary conditions and lattice points arbitrarily distributed on a half-circle, have been constructed using infinite MPSs related to suitable boundary CFTs and corresponding null fields [44]. Again, these CFT-inspired generalizations of the HS chain with open boundary conditions become integrable [44] and, in fact, exactly solvable [45], only for some special choices of the lattice points, but none of them possess the translational invariance of the original HS chain.…”