Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors

Abstract

In this paper we consider the spin 1/2 highest weight representations for the 6-vertex Yang-Baxter algebra on a finite lattice and analyze the integrable quantum models associated to the antiperiodic transfer matrix. For these models, which in the homogeneous limit reproduces the XXZ spin 1/2 quantum chains with antiperiodic boundary conditions, we obtain in the framework of Sklyanin's quantum separation of variables (SOV) the following results: I) The complete characterization of the transfer matrix spectrum (eigenvalues/eigenstates) and the proof of its simplicity. II) The reconstruction of all local operators in terms of Sklyanin's quantum separate variables. III) One determinant formula for the scalar products of separates states, the elements of the matrix in the scalar product are sums over the SOV spectrum of the product of the coefficients of the states. IV) The form factors of the local spin operators on the transfer matrix eigenstates by a one determinant formula given by simple modifications of the scalar product formula.

29 pages

References in corpus (57)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Separation of Variables. New Trends.
• How Algebraic Bethe Ansatz works for integrable model
• Applied Conformal Field Theory
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Computation of dynamical correlation functions of Heisenberg chains in a field
• On the quantum inverse scattering problem
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Quantum Inverse Scattering Method. Selected Topics
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Algebraic Structures Related to Reflection Equations
• Functional relations and Bethe Ansatz for the XXZ chain
• Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity
• Correlation functions of the open XXZ chain I
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
• Quantization of Solitons and the Restricted Sine-Gordon Model
• Spontaneous magnetization of the XXZ Heisenberg spin-1/2 chain
• Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
• Surface free energy of the open XXZ spin-1/2 chain
• Transfer matrix functional relations for the generalized tau_2(t_q) model
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• Counting the local fields in SG theory.
• 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
• The space of local operators in perturbed conformal field theories,
• The XXZ model with anti-periodic twisted boundary conditions
• Correlation functions of the higher spin XXX chains
• Structure of Matrix Elements in Quantum Toda Chain
• Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models
• Baxter-Bazhanov-Stroganov model: Separation of Variables and Baxter Equation
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Form factors of integrable Heisenberg (higher) spin chains
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in $1+1$-dimensional quantum field theory
• The connection between statistical mechanics and quantum field theory
• Matrix elements of the operator T\bar{T} in integrable quantum field theory
• On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain
• On the form factors of local operators in the lattice sine-Gordon model
• A Q-operator for the twisted XXX model
• The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
• Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory
• Finite Volume Spectrum of Sine-Gordon Model and its Restrictions
• Counting minimal form factors of the restricted sine-Gordon model
• Fermionic screening operators in the sine-Gordon model
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• On Form Factors of the conjugated field in the non-linear Schröodinger model
• Fermionic basis for space of operators in the XXZ model
• A lattice model related to the nonlinear Schroedinger equation
• Finite Size Effects in Integrable Quantum Field Theories
• Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model
• Boson decay and the dynamical structure factor for the XXZ chain at finite magnetic field
• Low-$T$ asymptotic expansion of the solution to the Yang-Yang equation

Cited by in corpus (74)

• An introduction to integrable techniques for one-dimensional quantum systems
• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• The half-infinite XXZ chain in Onsager's approach
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• On quantum separation of variables
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• 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
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• 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
• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• The 8-vertex model with quasi-periodic boundary conditions
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• A new integral representation for the scalar products of Bethe states for the XXX spin chain
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• On Scalar Products in Higher Rank Quantum Separation of Variables
• On quantum separation of variables beyond fundamental representations
• Reflection algebra and functional equations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Exact solution of the XXX Gaudin model with the generic open boundaries
• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• On Separation of Variables for Reflection Algebras
• Off-diagonal Bethe Ansatz on the $so(5)$ spin chain
• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• Correlation functions by Separation of Variables: the XXX spin chain
• Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Calculating eigenvalues of many-body systems from partition functions
• Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition
• Twisted Heisenberg chain and the six-vertex model with DWBC
• Exact solution of an su(n) spin torus
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Off-diagonal Bethe Ansatz for the $D_3^{(1)}$ model
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition
• Bethe states of the trigonometric SU(3) spin chain with generic open boundaries
• A novel class of translationally invariant spin chains with long-range interactions
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit
• Bethe ansatz inside Calogero-Sutherland models
• Off-diagonal approach to the exact solution of quantum integrable systems
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
• Separation of variables for higher rank integrable models: review of recent progress
• Bethe States of the integrable spin-s chain with generic open boundaries
• Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3
• Correlation functions of the XXZ spin chain with the twisted boundary condition
• The scalar product of XXZ spin chain revisited. Application to the ground state at $\Delta =-1/2$
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint
• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
• On the solutions of the $Z_n$-Belavin model with arbitrary number of sites
• On the equilibrium measure for the Lukyanov integral