Related papers: Applying matrix product operators to model systems…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
Matrix Product State (MPS) wavefunctions have many applications in quantum information and condensed matter physics. One application is to represent states in the thermodynamic limit directly, using a small set of position independent…
Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
A systematic and compact treatment of arbitrary $su(2)$ invariant spin-$s$ quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS…
We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix…
Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…
We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
The power of matrix product states to describe infinite-size translational-invariant critical spin chains is investigated. At criticality, the accuracy with which they describe ground state properties of a system is limited by the size…
Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…
Quantum trajectories and superoperator algorithms implemented within the matrix product state (MPS) framework are powerful tools to simulate the real-time dynamics of open dissipative quantum systems. As for the unitary case, the reachable…
Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains,…
We propose a method to simulate the real time evolution of one dimensional quantum many-body systems at finite temperature by expressing both the density matrices and the observables as matrix product states. This allows the calculation of…
We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in…
We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a…
We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce…
Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…
The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol…
Consider the $n!$ different unitary matrices that permute $n$ $d$-dimensional quantum systems. If $d\geq n$ then they are linearly independent. This paper discusses a sense in which they are approximately orthogonal (with respect to the…