Related papers: Post-Matrix Product State Methods: To tangent spac…
We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time…
We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…
We show how to simulate numerically both the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems and it is based on two ideas: (a) a representation…
Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
We analyze entanglement in the family of translationally-invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by SLOCC transformations, a central question in entanglement…
An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices leads to the…
We propose a new notion of the formal tangent space to the Wasserstein space $\mathcal{P}(X)$ at a given measure. Modulo an integrability condition, we say that this tangent space is made of functions over $X$ which are valued in the…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
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…
We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such…
Matrix-product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method…
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…
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…
A variational ansatz for momentum eigenstates of translation invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient implementation (cubic scaling in…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
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…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…