Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions

Abstract

We present a generalization of the coordinate Bethe ansatz that allows us to solve integrable open XXZ and ASEP models with non-diagonal boundary matrices, provided their parameters obey some relations. These relations extend the ones already known in the literature in the context of algebraic or functional Bethe ansatz. The eigenvectors are represented as sums over cosets of the $B{C}_n$ Weyl group.

arXiv commenttypos corrected, references updated, accepted in J. Stat. Mech

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• 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
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• A reverse duality for the ASEP with open boundaries
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
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• On Separation of Variables for Reflection Algebras
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Long time asymptotics of the totally asymmetric simple exclusion process
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• Markov duality and Bethe ansatz formula for half-line open ASEP
• KPZ fluctuations in finite volume
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• 3-state Hamiltonians associated to solvable 33-vertex models
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• 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
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• Particle current fluctuations in a variant of asymmetric Glauber model
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• Inhomogeneous discrete-time exclusion processes
• A note on a boundary sine-Gordon model at the free-Fermion point