Twisted Yangian symmetry of the open Hubbard model

Abstract

We show that, in the open Hubbard model with integrable boundary conditions, the bulk Yangian symmetry is broken to a twisted Yangian. We prove that the associated charges commute with the Hamiltonian and the reflection matrix, and that they form a coideal subalgebra.

How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models

“…It would be interesting to see if one can gain further insight into the unusual structure of the Hubbard model's known integrable boundaries [8,29,30] and perhaps obtain new ones. …”

The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model

“…This model was shown to be quantum integrable when imposing both periodic and open boundary conditions [1,11], the latter leading to a twisted Yangian symmetry [9]. Its R-matrix, which we shall denote as R, can be identified as a linear combination of tensor products of two free fermion model R-matrices, one for each spin layer [17].…”

“…However, just as in the case of other integrable open boundaries [9], there exists a subtlety: one must make use of the Yangian automorphism J 1 → J 1 + µJ 0 . In addition, the right Yangian copy is obtained not only through the map (2.8) but also by changing U to −U .…”

Fusion for AdS/CFT boundary S-matrices

“…[21,22]); and AdS/CFT boundary S-matrices for bound states have also been determined [23,24,25]. (See also [26,27,28,29,30,31] and references therein.) The main purpose of this note is to propose a new fusion formula for boundary S-matrices, which generates two-particle bound-state AdS/CFT boundary S-matrices from the fundamental one.…”