Related papers: Matrix Product States for Interacting Particles wi…
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…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones, -a situation advocated recently to be relevant for bird…
We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study…
We propose and analyze a method for efficient dissipative preparation of matrix product states that exploits their symmetry properties. Specifically, we construct an explicit protocol that makes use of driven-dissipative dynamics to prepare…
The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a…
For a large class of inhomogeneous interacting particle systems (IPS) on a lattice we develop a rigorous method for mapping them onto homogeneous IPS. Our novel approach provides a direct way of obtaining the statistical properties of such…
Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are…
We analyse the stochastic comparison of interacting particle systems allowing for multiple arrivals, departures and non-conservative jumps of individuals between sites. That is, if $k$ individuals leave site $x$ for site $y$, a possibly…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
We consider partial exclusion processes~(PEPs) on the one-dimensional square lattice, that is, a system of interacting particles where each particle random walks according to a jump rate satisfying an exclusion rule that allows up to a…
We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations (quantum filters) for an arbitrary quantum system probed by a bosonic input field in this class of states. We show that this…
It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these…
We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground…
In this paper, we construct under general assumptions the stochastic dynamics of an interacting particle system in a bounded domain $\Omega$ with sticky boundary. Under appropriate conditions on the interaction the constructed process…
We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without…
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…
Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved…
We investigate a non-Poissonian version of the asymmetric simple exclusion process, motivated by the observation that coarse-graining the interactions between particles in complex systems generically leads to a stochastic process with a…
We provide an exact construction of interaction Hamiltonians on a one-dimensional lattice which grow as a polynomial multiplied by an exponential with the lattice site separation as a matrix product operator (MPO), a type of one-dimensional…