Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz

Abstract

We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the ASEP Markov matrix can be expressed as traces of products of non-commuting operators. We derive the relations between the operators involved and show that they generate a quadratic algebra. Our construction provides explicit finite dimensional representations for the generators of this algebra.

arXiv comment16 pages

References in corpus (10)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Spectral gap of the totally asymmetric exclusion process at arbitrary filling
• A Spin Chain Primer
• Exact solutions of exactly integrable quantum chains by a matrix product ansatz
• The Bethe ansatz as a matrix product ansatz
• A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
• Dynamic Matrix Ansatz for Integrable Reaction-Diffusion Processes
• Hidden symmetries in the asymmetric exclusion process

Cited by in corpus (27)

• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Some Exact Results for the Exclusion Process
• Vertex models, TASEP and Grothendieck polynomials
• Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
• Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Temporal evolution of product shock measures in TASEP with sublattice-parallel update
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Exactly solvable interacting vertex models
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• Dual wavefunction of the Felderhof model
• Stochastic strong zero modes and their dynamical manifestations
• Family of Commuting Operators for the Totally Asymmetric Exclusion Process
• Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice
• From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation
• Asymmetric exclusion model with impurities
• Particle current fluctuations in a variant of asymmetric Glauber model
• Dual wavefunction of the symplectic ice
• Matrix Product States for Interacting Particles without Hardcore Constraints
• Asymmetric exclusion model with several kinds of impurities
• A note on a boundary one point function for the six vertex model with reflecting end
• Matrix product solution of the stationary states of two-species open zero range processes