Quantum Deformations of the One-Dimensional Hubbard Model

Abstract

The centrally extended superalgebra psu(2|2)xR^3 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 U_q(psu(2|2)xR^3) 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.

58 pages, v2: comments on Alcaraz-Bariev cases A+- extended, references added, v3: addresses corrected

References in corpus (54)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• New Exactly Solvable Model of Strongly Correlated Electrons Motivated by High T_c Superconductivity
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• On String S-matrix, Bound States and TBA
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Deformations of N=4 SYM and integrable spin chain models
• A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
• The Quantum Inverse Scattering Method for Hubbard-like Models
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• On the Hopf algebra structure of the AdS/CFT S-matrix
• The Yangian symmetry of the Hubbard Model
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• On spin chains and field theories
• The magnon kinematics of the AdS/CFT correspondence
• Algebraic Bethe Ansatz for gl(2,1) Invariant 36-Vertex Models
• A new integrable two parameter model of strongly correlated electrons in one dimension
• One parameter family of an integrable $spl(2|1)$ vertex model : Algebraic Bethe ansatz approach and ground state structure
• $U_{q}osp(2,2)$ Lattice Models
• Algebraic Bethe ansatz approach for the one-dimensional Hubbard model
• Classical r-matrix of the su(2|2) SYM spin-chain
• Integrable Electron Model with Correlated Hopping and Quantum Supersymmetry
• A Secret Symmetry of the AdS/CFT S-matrix
• The Asymptotic Spectrum of the N=4 Super Yang-Mills Spin Chain
• Thermodynamics of an integrable model for electrons with correlated hopping
• Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb-Wu equations
• The su(N) Hubbard model
• On the solution of a supersymmetric model of correlated electrons
• On the Scattering Phase for AdS_5 x S^5 Strings
• Interpolation between Hubbard and supersymmetric t-J models. Two-parameter integrable models of correlated electrons
• Twisted Quantum Affine Superalgebra $U_q[sl(2|2{)}^{(2)}]$, $U_q[osp(2|2)]$ Invariant R-matrices and a New Integrable Electronic Model
• The Leigh-Strassler Deformation and the Quest for Integrability
• Exact integrability of the su(n) Hubbard model
• A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)
• Exact solution of a one-dimensional fermion model with interchain tunneling
• Finite-Dimensional Representations of the Quantum Superalgebra U${}_q$[gl(2/2)]: II. Nontypical representations at generic $q$
• A New Solution of the Supersymmetric TJ Model by Means of the Quantum Inverse Scattering Method
• On the integrability of the SU(N) Hubbard model
• Finite-Dimensional Representations of the Quantum Superalgebra U${}_q$[gl(2/2)]: I. Typical representations at generic $q$
• Algebraic Bethe ansatz for an integrable U_q[Sl(n|m)] vertex model with mixed representations
• Algebraic Bethe Ansatz for Integrable Extended Hubbard Models Arising from Supersymmetric Group Solutions

Cited by in corpus (97)

• An integrable deformation of the AdS_5 x S^5 superstring action
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• On deformations of AdS_n x S^n supercosets
• An Integrable Deformation of the AdS5 x S5 Superstring
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Yang-Baxter sigma models based on the CYBE
• The S-matrix of String Bound States
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Towards integrability for AdS3/CFT2
• A Jordanian deformation of AdS space in type IIB supergravity
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• The classical origin of quantum affine algebra in squashed sigma models
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• The Quantum Deformed Mirror TBA I
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• The spectral problem for strings on twisted AdS_5 x S^5
• The Quantum Deformed Mirror TBA II
• A deformation of quantum affine algebra in squashed WZNW models
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• Yangians, S-matrices and AdS/CFT
• Yang-Baxter and the Boost: splitting the difference
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• A Relativistic Relative of the Magnon S-Matrix
• Representations of Quantum Affine Superalgebras
• Non-split and split deformations of AdS_5
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Type IIB supergravity solution for the T-dual of the eta-deformed AdS_5 x S^5 superstring
• The S-Matrix of AdS/CFT and Yangian Symmetry
• On the perturbative S-matrix of generalized sine-Gordon models
• Infinitely dimensional Lax structure for one-dimensional Hubbard model
• Yangian of AdS3/CFT2 and its deformation
• The Bethe Ansatz Equations for Reflecting Magnons
• Pulsating strings on $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Superspin chains and supersymmetric gauge theories
• Integrability of the eta-deformed Neumann-Rosochatius model
• RTT realization of quantum affine superalgebras and tensor products
• The Bound State S-matrix of the Deformed Hubbard Chain
• Secret Symmetries in AdS/CFT
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• Critical Properties of an Integrable Supersymmetric Eletronic Model
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Structure of the string R-matrix
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Integrable strings for AdS/CFT
• Hubbard-Shastry lattice models
• Popcorn Drude weights from quantum symmetry
• Integrable deformations of AdS/CFT
• Maximally extended sl(2|2) as a quantum double
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• Finite-size effect of η-deformed AdS_5 x S^5 at strong coupling
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Note on Centrally Extended su(2/2) and Serre Relations
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• A variational approach for the Quantum Inverse Scattering Method
• The splitting of electrons and violation of the Luttinger sum rule
• Quantum Groups as Global Symmetries
• Integrable Hopf twists, marginal deformations and generalised geometry
• A range three elliptic deformation of the Hubbard model
• On the Semi-Classical Limit of Scalar Products of the XXZ Spin Chain
• The Quantum Affine Origin of the AdS/CFT Secret Symmetry
• Bethe Ansatz for Quantum-Deformed Strings
• Pohlmeyer reduction for superstrings in AdS space
• NLIE for the Sausage model
• The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• Quantum deformation of cubic string field theory
• Yang-Baxter deformations of the flat space string
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Twisted Yangian symmetry of the open Hubbard model
• Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain
• Pulsating string solution and stability in two parameter $\chi$-deformed background
• Algebro-Geometric approach for a centrally extended U_q[sl(2|2)] R-matrix