Related papers: Approximating Relativistic Quantum Field Theories …
We present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered…
Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a…
Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective…
The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the…
Tensor network states, especially Matrix Product States (MPS), are crucial tools for studying how particles in large quantum systems are entangled with each other. MPS are particularly effective for modeling systems in one-dimensional…
A classification of SU(2)-invariant Projected Entangled Paired States (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al.~\cite{Mambrini2016}. It is not clear whether such…
We study the antiferromagnetic kagome Heisenberg model with additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of optimization algorithm in the…
A way of constructing continuous matrix product states (cMPS) for coupled fields is presented here. The cMPS is a variational \emph{ansatz} for the ground state of quantum field theories in one dimension. Our proposed scheme is based in the…
An important class of model Hamiltonians for investigation of topological phases of matter consists of mobile, interacting particles on a lattice subject to a semi-classical gauge field, as exemplified by the bosonic Harper-Hofstadter…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
Fermionic Gaussian Projected Entangled Pair States are fermionic tensor network state constructions which describe the physics of ground states of non-interacting fermionic Hamiltonians. As non-interacting states, one may study and analyze…
A simple, general and practically exact method, Entanglement Perturbation Theory (EPT), is formulated to calculate the ground states of 2D macroscopic quantum systems with translational symmetry. An emphasis will be placed on the…
We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions…
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure…
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
We discuss the geometry of a class of tensor network states, called projected entangled pair states in the Physics literature. We provide initial results towards a question of Verstraete and Rizzi regarding the tensor network state of an $M…
We develop an improved variant of $U(1)$-symmetric infinite projected entangled-pair state (iPEPS) ansatz to investigate the ground state phase diagram of the spin-$1/2$ square $J_{1}-J_{2}$ Heisenberg model. In order to improve the…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.