Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1412.3292 · Journal of High Energy Physics

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

Alejandro De La Rosa Gomez

Published Apr 1, 2015• 3 citations
arXivHTMLPDF

Abstract

We show that the particle-hole transformation in the Hubbard model has a crucial role in relating Shastry’s R-matrix to the AdS/CFT S-matrix. In addition, we construct an achiral boundary for the open Hubbard chain which possesses twisted Yangian symmetry.
DOI
10.1007/jhep04(2015)063

Related papers

Twisted Yangian symmetry of the open Hubbard model

Alejandro De La Rosa Gomez, Niall J MacKay

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.

arXiv:1404.2095•Journal of Physics A Mathematical and Theoretical•Jul 10, 2014•5 citations

Symmetries of integrable open boundaries in the Hubbard model and other spin chains.

Alejandro de la Rosa

We proceed to study the symmetries of integrable open boundaries in the one dimensional Hubbard model, the Heisenberg XXX spin chain and Inozemtsev's hyperbolic spin chain. \nFor the Hubbard model, we show that when placed on the left half-line, the known integrable open boundaries (a magnetic field and chemical potential) break the bulk Yangian symmetry to a twisted Yangian corresponding to the (sl2; u1) symmetric pair. Furthermore, we consider two additional boundaries, corresponding to the symmetric pairs (so4; sl2) and (sl2; sl2) and construct their twisted Yangian symmetries. This provides a step forward in the classification of integrable boundaries of the open Hubbard model. We conclude our study of this model by examining the symmetries of its bulk and open SU(n) generalisation. \n \nFor the Heisenberg XXX spin chain and Inozemtsev's hyperbolic spin chain we construct a procedure to, given the integrable bulk models, systematically obtain \ntheir integrable boundaries and corresponding Yangian symmetries for the symmetric pairs (sl2; u1); (so4; sl2) and (sl2; sl2). We call this method `folding', and it is \nmotivated by the wish to study integrable boundaries for long-range spin chains. We test this procedure by first applying it on the Heisenberg XXX spin chain and confirming it reproduces well known results. We then apply the folding to Inozemtsev's hyperbolic spin chain and classify its integrable open boundaries and their twisted Yangian symmetries.

•Jun 12, 2017•0 citations

Quantum deformations of the one-dimensional Hubbard model

Niklas Beisert, Peter Koroteev

The centrally extended superalgebra was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation and derive the fundamental R -matrix. From the latter we deduce an integrable spin-chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.

arXiv:0802.0777•Journal of Physics A Mathematical and Theoretical•May 28, 2008•137 citations

BoundaryS-matrices for the open Hubbard chain with boundary fields

Osamu Tsuchiya

Using the method introduced by Grisaru et al , boundary S-matrices for the physical excitations of the open Hubbard chain with boundary fields are studied. In contrast to the open supersymmetric t-J model, the boundary S-matrix for the charge excitations depend on the boundary fields though the boundary fields do not break the spin-SU(2) symmetry.

arXiv:cond-mat/9701002•Journal of Physics A Mathematical and General•Apr 21, 1997•4 citations

The Yangian symmetry of the Hubbard model

Fabian H. L. Eßler, Holger Frahm, Frank Göhmann +2 more

In this chapter we will reveal another piece of the algebraic structure of the Hubbard model. As was first observed by Uglov and Korepin [462], the Hubbard Hamiltonian on the infinite line is invariant under the action of the direct sum of two so-called Yangian quantum groups, extending the rotational and the η-pairing su(2) symmetries we encountered earlier. Following [172] we shall address the issue in a more general context. We present two pairs of fermionic representations of the Y(su(2)) Yangian quantum group which commute with the trigonometric [162] and hyperbolic [40, 41] versions of a Hubbard Hamiltonian with non-nearest-neighbour hopping. In both cases the two representations are also mutually commuting, hence can be combined into a representation of Y(su(2))⊕Y(su(2)). The generators of the Yangian symmetry of the ordinary Hubbard model (with nearest-neighbour hopping) and of a number of other interesting models like the Haldane-Shastry spin-chain [194, 394] are obtained as special cases of our general result. Introduction Quantum groups were introduced by Drinfeld [107, 109]. His original intention was to put what we called the Yang-Baxter algebra into the mathematically more conventional context of Hopf algebras. The Yangians are special quantum groups. Their representation theory [80, 81] is intimately related to the classification of integrable quantum systems with rational R -matrices.

Cambridge University Press eBooks•Feb 7, 2005•0 citations

A quantum affine algebra for the deformed Hubbard chain

Niklas Beisert, W. Galléas, Takuya Matsumoto

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R -matrix and the Yangian of a centrally extended superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R -matrix has recently been found. This R -matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine algebra in two special limits.

arXiv:1102.5700•Journal of Physics A Mathematical and Theoretical•Aug 22, 2012•44 citations
We proceed to study the symmetries of integrable open boundaries in the one dimensional Hubbard model, the Heisenberg XXX spin chain and Inozemtsev's hyperbolic spin chain. \nFor the Hubbard model, we show that when placed on the left half-line, the known integrable open boundaries (a magnetic field and chemical potential) break the bulk Yangian symmetry to a twisted Yangian corresponding to the (sl2; u1) symmetric pair. Furthermore, we consider two additional boundaries, corresponding to the symmetric pairs (so4; sl2) and (sl2; sl2) and construct their twisted Yangian symmetries. This provides a step forward in the classification of integrable boundaries of the open Hubbard model. We conclude our study of this model by examining the symmetries of its bulk and open SU(n) generalisation. \n \nFor the Heisenberg XXX spin chain and Inozemtsev's hyperbolic spin chain we construct a procedure to, given the integrable bulk models, systematically obtain \ntheir integrable boundaries and corresponding Yangian symmetries for the symmetric pairs (sl2; u1); (so4; sl2) and (sl2; sl2). We call this method `folding', and it is \nmotivated by the wish to study integrable boundaries for long-range spin chains. We test this procedure by first applying it on the Heisenberg XXX spin chain and confirming it reproduces well known results. We then apply the folding to Inozemtsev's hyperbolic spin chain and classify its integrable open boundaries and their twisted Yangian symmetries.
The centrally extended superalgebra was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation and derive the fundamental R -matrix. From the latter we deduce an integrable spin-chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.
In this chapter we will reveal another piece of the algebraic structure of the Hubbard model. As was first observed by Uglov and Korepin [462], the Hubbard Hamiltonian on the infinite line is invariant under the action of the direct sum of two so-called Yangian quantum groups, extending the rotational and the η-pairing su(2) symmetries we encountered earlier. Following [172] we shall address the issue in a more general context. We present two pairs of fermionic representations of the Y(su(2)) Yangian quantum group which commute with the trigonometric [162] and hyperbolic [40, 41] versions of a Hubbard Hamiltonian with non-nearest-neighbour hopping. In both cases the two representations are also mutually commuting, hence can be combined into a representation of Y(su(2))⊕Y(su(2)). The generators of the Yangian symmetry of the ordinary Hubbard model (with nearest-neighbour hopping) and of a number of other interesting models like the Haldane-Shastry spin-chain [194, 394] are obtained as special cases of our general result. Introduction Quantum groups were introduced by Drinfeld [107, 109]. His original intention was to put what we called the Yang-Baxter algebra into the mathematically more conventional context of Hopf algebras. The Yangians are special quantum groups. Their representation theory [80, 81] is intimately related to the classification of integrable quantum systems with rational R -matrices.
The integrable structure of the one-dimensional Hubbard model is based on Shastry's R -matrix and the Yangian of a centrally extended superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R -matrix has recently been found. This R -matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine algebra in two special limits.