Related papers: Matrix Product Ground States for Asymmetric Exclus…
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…
This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstra{\ss} canonical form and, thus, be decoupled into differential…
The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric…
Duality transformations reveal unexpected equivalences between seemingly distinct models. We introduce an out-of-equilibrium generalisation of matrix product operators to implement duality transformations in one-dimensional boundary-driven…
The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of…
The asymmetric simple exclusion process (ASEP) with periodic boundary conditions is investigated for shuffled dynamics. In this type of update, in each discrete timestep the particles are updated in a random sequence. Such an update is…
We study a one-parameter generalization of the symmetric simple exclusion process on a one dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…
Markov processes on the lattices with arbitrary dimension are omnipresent in statistical mechanics; however their algebraic description is complete only in dimension 1, for which linear algebra provides many tools complementary to the…
We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…
The basic model of the non-equilibrium low dimensional physics the so-called totally asymmetric exclusion process is related to the 'crystalline limit' ($q\to\infty$) of the $SU_q(2)$ quantum algebra. Using the quantum inverse scattering…
Products of random matrices in the $(\max,+)$ algebra are used as a model for a class of discrete event dynamical systems. J. Mairesse proved that such a system couples in finite times with a unique stationary regime if and only if it has a…
The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically induces phase separation in a range of densities. In the particlewise case the existence of…
We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans,…
We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are…
Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill…
We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. This greatly…
Quantum many-body systems divide into a variety of phases with very different physical properties. The question of what kind of phases exist and how to identify them seems hard especially for strongly interacting systems. Here we make an…
We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have…