English
Related papers

Related papers: Using matrix product states to study the dynamical…

200 papers

We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…

Computational Physics · Physics 2023-08-08 Xing-Yu Zhang , Shuang Liang , Hai-Jun Liao , Wei Li , Lei Wang

Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of…

Statistical Mechanics · Physics 2013-07-18 M. L. Wall , Lincoln D. Carr

Kinetically constrained models (KCMs) are models of glass formers based on the concept of dynamic facilitation. This concept accounts for many of the characteristics of the glass transition. KCMs usually display a combination of simple…

Statistical Mechanics · Physics 2007-05-23 Stephen Whitelam , Juan P. Garrahan

By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new…

Strongly Correlated Electrons · Physics 2022-08-31 Guglielmo Lami , Giuseppe Carleo , Mario Collura

We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states…

Quantum Physics · Physics 2016-01-06 Se-Wan Ji , Jaehak Lee , Jiyong Park , Hyunchul Nha

This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can…

Mathematical Physics · Physics 2021-11-11 Tristan Gautié

In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such…

Dynamical Systems · Mathematics 2011-11-08 Massimo Fornasier , Jan Haskovec , Jan Vybiral

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of…

Other Condensed Matter · Physics 2008-08-18 Gregory M. Crosswhite , Andrew C. Doherty , Guifre Vidal

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Machine Learning · Computer Science 2024-03-15 Vladimir R. Kostic , Pietro Novelli , Riccardo Grazzi , Karim Lounici , Massimiliano Pontil

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…

Quantum Physics · Physics 2025-01-06 Wen-Yuan Liu , Si-Jing Du , Ruojing Peng , Johnnie Gray , Garnet Kin-Lic Chan

Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…

Strongly Correlated Electrons · Physics 2017-05-24 Jutho Haegeman , Frank Verstraete

The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…

Quantum Physics · Physics 2008-11-26 Jose I. Latorre

We demonstrate the power of 2D tensor networks for obtaining large deviation functions of dynamical observables in a classical nonequilibrium setting. Using these methods, we analyze the previously unstudied dynamical phase behavior of the…

Statistical Mechanics · Physics 2020-10-07 Phillip Helms , Garnet Kin-Lic Chan

Motivation: We consider continuous-time Markov chains that describe the stochastic evolution of a dynamical system by a transition-rate matrix $Q$ which depends on a parameter $\theta$. Computing the probability distribution over states at…

In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…

Statistical Mechanics · Physics 2019-06-26 Marko Medenjak , Vladislav Popkov , Tomaž Prosen , Eric Ragoucy , Matthieu Vanicat

We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in…

Strongly Correlated Electrons · Physics 2024-06-26 J. W. Cai , Q. N. Chen , H. H. Zhao , Z. Y. Xie , M. P. Qin , Z. C. Wei , T. Xiang

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

Machine Learning · Computer Science 2020-06-08 Anna Shalova , Ivan Oseledets

In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…

Numerical Analysis · Mathematics 2025-07-10 Javier Lopez-Piqueres , Jing Chen

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…

Quantum Physics · Physics 2008-04-29 Karoline Wiesner , James P. Crutchfield

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…

Quantum Physics · Physics 2022-10-06 Xiao-Qi Sun , Tamra Nebabu , Xizhi Han , Michael O. Flynn , Xiao-Liang Qi