Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models

Abstract

We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous $g{l}_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model both defined with quasi-periodic twisted boundary conditions given by twist matrices having simple spectrum. The SoV bases are obtained by using the integrable structure of these quantum models,i.e. the associated commuting transfer matrices, following the general scheme introduced in [1]; namely, they are given by set of states generated by the multiple action of the transfer matrices on a generic co-vector. The existence of such SoV bases implies that the corresponding transfer matrices have non degenerate spectrum and that they are diagonalizable with simple spectrum if the twist matrices defining the quasi-periodic boundary conditions have that property. Moreover, in these SoV bases the resolution of the transfer matrix eigenvalue problem leads to the resolution of the full spectral problem, i.e. both eigenvalues and eigenvectors. Indeed, to any eigenvalue is associated the unique (up to a trivial overall normalization) eigenvector whose wave-function in the SoV bases is factorized into products of the corresponding transfer matrix eigenvalue computed on the spectrum of the separate variables. As an application, we characterize completely the transfer matrix spectrum in our SoV framework for the fundamental $g{l}_{1|2}$ supersymmetric integrable model associated to a special class of twist matrices. From these results we also prove the completeness of the Bethe Ansatz for that case. The complete solution of the spectral problem for fundamental inhomogeneous $g{l}_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model under the general twisted boundary conditions will be addressed in a future publication.

arXiv comment53 pages, v3 - several footnotes and remarks added, references added and some further typos corrected

References in corpus (151)

• Review of AdS/CFT Integrability: An Overview
• A Mott insulator of fermionic atoms in an optical lattice
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Separation of Variables. New Trends.
• The su(2|2) Dynamic S-Matrix
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Quantum spectral curve for AdS_5/CFT_4
• Correlation Functions of the XXZ model for $\Delta <-1$
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• Diffusion and ballistic transport in one-dimensional quantum systems
• Computation of dynamical correlation functions of Heisenberg chains in a field
• On the quantum inverse scattering problem
• The one-dimensional Hubbard model: A reminiscence
• Tailoring Three-Point Functions and Integrability
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• T-systems and Y-systems in integrable systems
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• A Shortcut to the Q-Operator
• Form factor approach to dynamical correlation functions in critical models
• Planar N=4 Gauge Theory and the Hubbard Model
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Order to disorder transition in the XY-like quantum magnet Cs2CoCl4 induced by noncommuting applied fields
• XXZ chain with a boundary
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• The Quantum Inverse Scattering Method for Hubbard-like Models
• Master equation for spin-spin correlation functions of the XXZ chain
• Correlation functions of the open XXZ chain I
• Difference Equations in Spin Chains with a Boundary
• Separation of Variables in the open XXX chain
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• The Yangian symmetry of the Hubbard Model
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Baxter's Q-operators for supersymmetric spin chains
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Baxter's Q-operator for the homogeneous XXX spin chain
• The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties
• On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
• Nested Bethe ansatz for "all" closed spin chains
• Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Dynamical correlation functions of the XXZ spin-1/2 chain
• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
• Quantization of Solitons and the Restricted Sine-Gordon Model
• Correlation functions of the open XXZ chain II
• Separation of variables for the quantum SL(2,R) spin chain
• Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain
• Algebraic Bethe Ansatz for gl(2,1) Invariant 36-Vertex Models
• Quantum Group Representations and Baxter Equation
• Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
• Exercises with the universal R-matrix
• Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
• Quantum Integrability for Three-Point Functions
• Separation of variables for integrable spin-boson models
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Fast analytic solver of rational Bethe equations
• Bethe vectors of GL(3)-invariant integrable models
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Algebraic Bethe ansatz approach for the one-dimensional Hubbard model
• Integrable Boundary Conditions for the One-Dimensional Hubbard Model
• On The Baxter's Q - Operator for the XXX Spin Chain
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• Oscillator Construction of su(n|m) Q-Operators
• From Characters to Quantum (Super)Spin Chains via Fusion
• Dual Separated Variables and Scalar Products
• Highest coefficient of scalar products in SU(3)-invariant integrable models
• Analytic Bethe ansatz and functional equations for Lie superalgebra sl(r+1|s+1)
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Functional Bethe ansatz methods for the open XXX chain
• Tailoring Non-Compact Spin Chains
• Form factors in SU(3)-invariant integrable models
• On quantum separation of variables
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Equivalences between spin models induced by defects
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• The hexagon in the mirror: the three-point function in the SoV representation
• Separation of variables and scalar products at any rank
• Structure of Matrix Elements in Quantum Toda Chain
• GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame
• The Yangian Symmetry of the Hubbard Models with Variable Range Hopping
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• Analytical Bethe Ansatz for closed and open gl(M|N) super-spin chains in arbitrary representations and for any Dynkin diagram
• Baxter-Bazhanov-Stroganov model: Separation of Variables and Baxter Equation
• The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Discrete Hirota's equation in quantum integrable models
• Analytic Bethe Ansatz for 1-D Hubbard model and twisted coupled XY model
• The Sine-Gordon model revisited I
• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
• Antiperiodic dynamical 6-vertex model by separation of variables II: Functional equations and form factors
• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Three-Point Functions and su(1|1) Spin Chains
• Q-operators in the six-vertex model
• Form factors of local operators in a one-dimensional two-component Bose gas
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• On Bethe vectors in ${\mathfrak{gl}}_3$-invariant integrable models
• Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb-Wu equations
• Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model
• Analytic Bethe ansatz related to a one parameter family of finite dimensional representations of the Lie superalgebra sl(r+1|s+1)
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Problems with using separated variables for computing expectation values for higher ranks
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• The 8-vertex model with quasi-periodic boundary conditions
• The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Oscillator versus prefundamental representations II. Arbitrary higher ranks
• Oscillator versus prefundamental representations
• On the form factors of local operators in the lattice sine-Gordon model
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Microscopic approach to a class of 1D quantum critical models
• Quantum groups and functional relations for higher rank
• A review of the AdS/CFT Quantum Spectral Curve
• Nonlinear Integral Equations and high temperature expansion for the $U_q(\widehat{sl}(r+1|s+1))$ Perk-Schultz Model
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• A Q-operator for the twisted XXX model
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Algebraic Solution of the Hubbard Model on the Infinite Interval
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Determinant representations for form factors in quantum integrable models with GL(3)-invariant R-matrix
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Solutions of ${\mathfrak{gl}}_{m|n}$ XXX Bethe ansatz equation and rational difference operators
• On Separation of Variables for Reflection Algebras
• Non-diagonal boundary conditions for gl(1|1) super spin chains
• Fusion for the one-dimensional Hubbard model
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations

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• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Separation of variables for higher rank integrable models: review of recent progress
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory