Related papers: Algebraically contractible topological tensor netw…
We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition $(A,B)$ of the lattice…
Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to 'trace…
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…
Treating the infinite-dimensional Hilbert space of non-abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming…
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological…
The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor…
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…
It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…
We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The…
In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…
An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation of the abelian networks series of Bond and Levine (2016),…
We investigate the topological classification of the subgap bands induced in a two-dimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic or spiral alignments. The wave functions for these bands are…
Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called…
Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$…
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement…
We introduce a set of axioms for locally topologically ordered quantum spin systems in terms of nets of local ground state projections, and we show they are satisfied by Kitaev's Toric Code and Levin-Wen type models. For a locally…
Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretize gravity to incorporate it, because that would…