Related papers: Entanglement renormalization and topological order
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
The multiscale entanglement renormalization ansatz is applied to the study of boundary critical phenomena. We compute averages of local operators as a function of the distance from the boundary and the surface contribution to the ground…
We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral…
A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of…
Continuous tensor networks are variational wavefunctions proposed in recent years to efficiently simulate quantum field theories (QFTs). Prominent examples include the continuous matrix product state (cMPS) and the continuous multi-scale…
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…
We study the behavior of the R\'enyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that R\'enyi entropies of different index…
Identifying entanglement-based order parameters characterizing topological systems, in particular topological superconductors and topological insulators, has remained a major challenge for the physics of quantum matter in the last two…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
In this paper we prove, extend and review possible mappings between the two-dimensional Cluster state, Wen's model, the two-dimensional Ising chain and Kitaev's toric code model. We introduce a two-dimensional duality transformation to map…
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$…
We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state…
The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…
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…
We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete…
We present an revised geometric measure of entanglement (RGME). The revised version is an entanglement monotone. Some useful inequalities about RGME are deduced. For exemplification, we give the formulas of RGME for the two-parameter class…
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the…
We make an analysis of the two-dimensional U(1) lattice gauge theory with a $\theta$ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling…
We study the entanglement R\'{e}nyi $\alpha$-entropy (ER$\alpha $E) as the measure of entanglement. Instead of a single quantity in standard entanglement quantification for a quantum state by using the von Neumann entropy for the…