Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms

Abstract

We use the quantum separation of variable (SOV) method to construct the eigenstates of the open XXZ chain with the most general boundary terms. The eigenstates in the inhomogeneous case are constructed in terms of solutions of a system of quadratic equations. This SOV representation permits us to compute scalar products and can be used to calculate form factors and correlation functions.

32 pages

References in corpus (13)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Form factor approach to dynamical correlation functions in critical models
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• 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
• Correlation functions of the open XXZ chain II
• The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• 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
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables

Cited by in corpus (55)

• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• 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
• 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
• Antiperiodic dynamical 6-vertex model by separation of variables II: Functional equations and form factors
• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
• 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 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
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• On quantum separation of variables beyond fundamental representations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
• Exact solution of the XXX Gaudin model with the generic open boundaries
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• On Separation of Variables for Reflection Algebras
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
• Correlation functions by Separation of Variables: the XXX spin chain
• Calculating eigenvalues of many-body systems from partition functions
• Scalar product for the XXZ spin chain with general integrable boundaries
• Exact solution of an su(n) spin torus
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Inversion identities for inhomogeneous face models
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models
• On the complete-spectrum characterization of quantum integrable spin chains via the inhomogeneous T-Q relation
• Energy spectrum of interacting gas: cluster expansion method
• The solution of an open XXZ chain with arbitrary spin revisited
• 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
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Correlation functions of the XXZ spin chain with the twisted boundary condition
• Bethe States of the integrable spin-s chain with generic open boundaries
• Non-linear integral equations for the XXX spin-1/2 quantum chain with non-diagonal boundary fields
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint
• A note on a boundary sine-Gordon model at the free-Fermion point