Related papers: A hierarchy of topological tensor network states
For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive,…
We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using…
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
The entanglement entropy encodes fundamental characteristics of quantum many-body systems, and is particularly subtle in non-Hermitian settings where eigenstates generically become non-orthogonal. In this work, we find that negative…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers etc., can be considered as ``chaotic'' superpositions of mean-field basis states (Slater determinants, products of…
"Topological ordered" phases such as gapped quantum spin-liquids and fractional quantum Hall states possess ground state degeneracy on a torus. We show that the topological nature of this degeneracy has interesting consequences for the…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…
We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to…
In this paper, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S=S_G+S_F, with S_F the…
We introduce a two-dimensional network model that realizes a higher-order topological phase (HOTP). We find that in the HOTP the bulk and boundaries of the system are gapped, and a total of 16 corner states are protected by the combination…
This thesis contributes to the understanding of symmetry-enriched topological phases focusing on their descriptions in terms of tensor network states. The Projected Entangled Pair State (PEPS) formalism allows us to locally encode the main…
Long-range entanglement--the backbone of topologically ordered states--cannot be created in finite time using local unitary circuits, or equivalently, adiabatic state preparation. Recently it has come to light that single-site measurements…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic…