Related papers: Towards a Matrix Product Ansatz in Two Dimensions
We construct matrix product steady state for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of total number…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
We apply the Matrix Product Ansatz to study the Totally Asymmetric Simple Exclusion Process on a ring with a generalized discrete-time dynamics depending on two hopping probabilities, $p$ and $\tilde{p}$. The model contains as special cases…
It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These…
We obtain through a Matrix Product Ansatz (MPA) the exact solution of the most general $N$-state spin chain with $U(1)^N$ symmetry and nearest neighbour interaction. In the case N=6 this model contain as a special case the integrable SO(6)…
We present an explicit time-dependent matrix product ansatz (tMPA) which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of…
We will prove certain general relations in Matrix Product Ansatz for one dimensional stochastic systems, which are true in both random and sequential updates. We will derive general MPA expressions for the currents and current correlators…
A one-dimensional, driven lattice gas with a freely moving, driven defect particle is studied. Although the dynamics of the defect are simply biased diffusion, it disrupts the local density of the gas, creating nontrivial nonequilibrium…
The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…
We introduce a general model of stochastically generated matrix product states (MPS) in which the local tensors share a common distribution and form a strictly stationary sequence, without requiring spatial independence. Under natural…
Using the matrix product ansatz, we obtain solutions of the steady-state distribution of the two-species open one-dimensional zero range process. Our solution is based on a conventionally employed constraint on the hop rates, which…
Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not…
The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
The asymmetric simple exclusion process (ASEP) is a paradigmatic driven-diffusive system that describes the asymmetric diffusion of particles with hardcore interactions in a lattice. Although the ASEP is known as an exactly solvable model,…
We present an implementation of a continuous matrix product state for two-component fermions in one-dimension. We propose a construction of variational matrices with an efficient parameterization that respects the translational symmetry of…
We consider the dynamics of a single shock in a partially asymmetric simple exclusion process (PASEP) on a finite lattice with open boundaries in the sublattice-parallel updating scheme. We then construct the steady state of the system by…
Active matter has been intensely studied for its wealth of intriguing properties such as collective motion, motility-induced phase separation (MIPS), and giant fluctuations away from criticality. However, the precise connection of active…
Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…