Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models

Abstract

We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in

18 pages; Version to appear in J Phys A

References in corpus (11)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Matrix representation of the stationary measure for the multispecies TASEP
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Functional Bethe ansatz methods for the open XXX chain
• Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
• Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields
• Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction
• New results in the XXZ open spin chain

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• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
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• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Yang-Baxter integrable Lindblad equations
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Bethe Ansatz and Q-operator for the open ASEP
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• Relaxation rate of the reverse biased asymmetric exclusion process
• Long time asymptotics of the totally asymmetric simple exclusion process
• Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• KPZ fluctuations in finite volume
• Statistics of sums of correlated variables described by a matrix product ansatz
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Coordinate Bethe Ansätze for non-diagonal boundaries
• Particle current fluctuations in a variant of asymmetric Glauber model
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• General limit distributions for sums of random variables with a matrix product representation
• The solution of an open XXZ chain with arbitrary spin revisited
• Large deviations for correlated random variables described by a matrix product ansatz
• Inhomogeneous discrete-time exclusion processes
• Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model
• Lifted TASEP: long-time dynamics,generalizations, and continuum limit