Related papers: Tangent-space methods for uniform matrix product s…
We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with…
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 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…
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 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…
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…
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…
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…
The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with…
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…
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 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…
We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without…
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…
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…
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…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equations and identifiability. By an interplay of theorems from…
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…
We consider the problem of approximating ground states of one-dimensional quantum systems within the two most common variational ansatzes, namely the mean field ansatz and Matrix Product States. We show that both for mean field and for…