Matrix Product Eigenstates for One-Dimensional Stochastic Models and Quantum Spin Chains

Abstract

We show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can be written as matrix product states. This means that the weights in these states can be expressed as expectation values in a Fock representation of an algebra generated by $2m$ operators fulfilling $m^2$ quadratic relations which are defined by the Hamiltonian.

11 pages, Latex

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• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• A multi-species asymmetric simple exclusion process and its relation to traffic flow
• Yang-Lee Theory for a Nonequilibrium Phase Transition
• Bethe Ansatz Solution for a Defect Particle in the Asymmetric Exclusion Process
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Diffusion algebras
• N-species stochastic models with boundaries and quadratic algebras
• Exact results for one dimensional stochastic cellular automata for different types of updates
• Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem
• Matrix Product Operators for Sequence to Sequence Learning
• On the ubiquity of matrix-product states in one-dimensional stochastic processes with boundary interactions
• An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update
• Matrix Product Steady States as Superposition of Product Shock Measures in 1D Driven Systems
• Dyck Paths, Motzkin Paths and Traffic Jams
• A multi-species asymmetric exclusion process;steady state and correlation functions on a periodic lattice
• Integrable boundary conditions for multi-species ASEP
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• The asymmetric exclusion process: Comparison of update procedures
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Construction of a matrix product stationary state from solutions of finite size system
• Phase Transition in a Three-States Reaction-Diffusion System
• A Remark on Integrability of Stochastic Systems Solvable by Matrix Product Ansatz
• Exact stationary state for a deterministic high speed traffic model with open boundaries
• On Matrix Product States for Periodic Boundary Conditions
• Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update
• Particle redistribution and slow decay of correlations in hard-core fluids on a half-driven ladder
• One-dimensional irreversible aggregation with TASEP dynamics
• Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics
• Nonequilibrium transport and phase transitions in driven diffusion of interacting particles
• Matrix Product representation of the stationary state of the open Zero Range Process
• Transfer matrices for the totally asymmetric exclusion process
• A Family of Exactly-Solvable Driven-Diffusive Systems in One-dimension
• Valence bond ground states in quantum antiferromagnets and quadratic algebras
• Matrix product solution of the stationary states of two-species open zero range processes
• A stochastic model solvable without integrability