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The asymmetric simple exclusion process (ASEP) is a paradigm for non-equilibrium physics that appears as a building block to model various low-dimensional transport phenomena, ranging from intracellular traffic to quantum dots. We review…

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of…

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of…

We show how to generalize the concepts of identifying and classifying symmetry protected topological phases in 1D to the case of an arbitrary mixed state. The pure state concepts are reviewed using a concrete spin-1 model. For the mixed…

We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean…

We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the…

We study a one-dimensional anisotropic exclusion model describing particles moving deterministically on a ring with a single defect across which they move with probability 0 < q < 1. We show that the stationary state of this model can be…

In this note we discuss how the matrix product solution for the steady state of the harmonic process is obtained from the solutions already known in the literature, i.e. the closed-form expression derived in arXiv:2107.01720 and the nested…

A multi-species generalization of the asymmetric simple exclusion process (ASEP) is studied in ordered sequential and sub-lattice parallel updating schemes. In this model particles hop with their own specific probabilities to their…

We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the…

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…

We consider a multi-species generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for x and yth-class particles (x<y), the transition xy -> yx occurs with a rate independent from the values…

We analyze the dynamical phases of the current-biased 1D and multi-lane open asymmetric simple exclusion processes (ASEP), using matrix product states and the density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, we present…

In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…

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…

We give a combinatorial description of the stationary measure for a totally asymmetric exclusion process (TASEP) with second class particles, on either Z or on the cycle Z_N. The measure is the image by a simple operation of the uniform…

In this paper, we show how a fixed point based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we…

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…

Matrix product ansatz (MPA) is a powerful framework for constructing exact steady state weights of one dimensional non-equilibrium stochastic processes; but its generalization to higher dimensions is limited. Here, we introduce the MPA…