Related papers: Continuum limits of Matrix Product States
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete et al. in 2005 and characterize the tensors corresponding…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit states under experimental restrictions. We…
We study a class of multi-species ASEP with open boundaries. The boundaries are chosen in such a way that all species of particles interact non-trivially with the boundaries and are present in the stationary state. We give the exact…
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…
In approximate ground states obtained from imaginary-time evolution, the spectrum of the state -- its decomposition into exact energy eigenstates -- falls off exponentially with the energy. Here we consider the energy spectra of approximate…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
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 answer the question if the continuous product of square matrices $M(t)$ over $t\in [0,1]$ can be correctly defined. The case where all $M(t)$ are taken from a finite set $\Sigma$ is studied. We find necessary and sufficient conditions on…
We discuss some aspects of the continuum limit of some lattice models, in particular the $2D$ $O(N)$ models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume…
We argue that the natural way to generalise a tensor network variational class to a continuous quantum system is to use the Feynman path integral to implement a continuous tensor contraction. This approach is illustrated for the case of a…
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types…
The Ensemble Kalman Filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control--to--observable identification problems. In applications it may be required to enforce the solution to satisfy…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
We introduce an approach for understanding control policies represented as recurrent neural networks. Recent work has approached this problem by transforming such recurrent policy networks into finite-state machines (FSM) and then analyzing…
Reduction criteria for distillability is applied to general depolarized states and an explicit condition is found in terms of a characteristic polynomial of the density matrix. 3 $\times$ 3 bipartite systems are analyzed in some details.
We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states.…