Related papers: The Linear Span of Uniform Matrix Product States
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…
Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…
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…
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…
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 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…
Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…
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 develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the exactly-solvable Calogero-Moser model. We show the high…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way.…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These…
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 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 this paper, we consider a system of homogeneous algebraic equations in complex variables and their conjugates, which arise naturally from the range criterion for separability of PPT states. We examine systematically these equations to…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
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 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…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…