Related papers: Symmetries and field tensor network states
An efficient algorithm is developed for quantum spin tubes in the context of the tensor network representations. It allows to efficiently compute the ground-state fidelity per lattice site, which in turn enables us to identify quantum…
We investigate the tensor network representations of fermionic crystalline symmetry-protected topological (SPT) phases on two-dimensional lattices. As a mapping from virtual indices to physical indices, projected entangled-pair state (PEPS)…
We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor…
Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…
We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual,…
Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient…
Strongly correlated quantum many-body systems at low dimension exhibit a wealth of phenomena, ranging from features of geometric frustration to signatures of symmetry-protected topological order. In suitable descriptions of such systems, it…
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…
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…
We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral of an effective theory on a family of hyperbolic slices in the dual bulk geometry. The…
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.,…
Determination and characterization of criticality in two-dimensional (2D) quantum many-body systems belong to the most important challenges and problems of quantum physics. In this paper we propose an efficient scheme to solve this problem…
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…
We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation…
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…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…