Related papers: Post-Matrix Product State Methods: To tangent spac…
In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of…
We discuss various properties of the variational class of continuous matrix product states, a class of ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful…
Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continuum. To do this, we analyse a fine-graining renormalization…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a…
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…
We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under a careful treatment of the translational symmetry, eigen values of the transfer matrix defined in the…
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…
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…
We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows to extend the density matrix renormalization group and variational matrix product state formalism to quantum field…
We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this…
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 central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…
We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a…