Related papers: Applying matrix product operators to model systems…
Building on a previously introduced block Lanczos method, we demonstrate how to approximate any operator function of the form Trf (A) when the argument A is given as a Hermitian matrix product operator. This gives access to quantities that,…
A protocol to obtain the matrix product state representation of a class of boson states is introduced. The proposal is presented in the context of linear systems and is tested by performing simulations of a reference model. The method can…
We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…
We propose an efficient algorithm to numerically solve Anderson impurity problems using matrix product states. By introducing a modified chain mapping we obtain significantly lower entanglement, as compared to all previous attempts, while…
The ground-state properties of the S=1 Haldane-Shastry model are studied using a modified Lanczos algorithm and diagonalizing exactly small chains. We find evidence that, as for the antiferromagnetic Heisenberg model, the spectrum shows a…
For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…
We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($\phi^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply…
We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of 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…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional…
Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various…
We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting…
Ultracold atom experiments allow the study of topological insulators, such as the noninteracting Haldane model. In this work we study a generalization of the Haldane model with spin-spin on-site interactions that can be implemented on such…
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 propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
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…
Modeling open quantum systems -- quantum systems coupled to a bath -- is of value in condensed matter theory, cavity quantum electrodynamics, nanosciences and biophysics. The real-time simulation of open quantum systems was advanced…
Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…