Related papers: Matrix Product States for dynamical simulation of …
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices…
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G…
Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state…
We investigate entanglement properties of infinite 1D and 2D spin-1/2 quantum Ising and XXZ models. Tensor network methods (MPS in 1D and TERG and CTMRG in 2D) are used to model the ground state of the studied models. Different entanglement…
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…
A one-dimensional quantum spin model with the competing two-spin and three-spin interactions is investigated in the context of a tensor network algorithm based on the infinite matrix product state representation. The algorithm is an…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak…
We combine matrix-product state (MPS) and Mean-Field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between…
Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Given a gapped Hamiltonian of a spin chain, we give a polynomial-time algorithm for finding the degenerate ground space projector. The output is an orthonormal set of matrix product states that approximate the true ground space projector up…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We discuss how to analytically obtain an -- essentially infinite -- Matrix Product State (MPS) representation of the ground state of the XY model. On the one hand this allows to illustrate how the Ornstein-Zernike form of the correlation…
We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to 2 legged spin ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by the…
We study the non-equilibrium time evolution of the average transverse magnetisation and end-to-end correlation functions of the random Ising quantum chain. Starting with fully magnetised states, either in the $x$ or $z$ direction, we…
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…