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We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $\alpha$ over $G$. The detailed properties of the ground states are studied, and we find that the…

Strongly Correlated Electrons · Physics 2013-03-25 Yuting Hu , Yidun Wan , Yong-Shi Wu

Casini et al raise the issue that the entanglement entropy in gauge theories is ambiguous because its definition depends on the choice of the boundary between two regions.; even a small change in the boundary could annihilate the otherwise…

High Energy Physics - Theory · Physics 2015-07-02 Ling-Yan Hung , Yidun Wan

Understanding the behaviour of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy…

Strongly Correlated Electrons · Physics 2013-05-29 S. Iblisdir , D. Perez-Garcia , M. Aguado , J. Pachos

We consider various aspects of Kitaev's toric code model on a plane in the C^*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized…

Mathematical Physics · Physics 2011-06-03 Pieter Naaijkens

We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…

Computational Physics · Physics 2023-08-08 Xing-Yu Zhang , Shuang Liang , Hai-Jun Liao , Wei Li , Lei Wang

Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…

Quantum Physics · Physics 2021-05-26 Isaac H. Kim

We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order,…

Strongly Correlated Electrons · Physics 2026-05-28 Lea E. Bottini , Clement Delcamp , Edmund Heng , Campbell K. McLauchlan , Dominic J. Williamson

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our…

Quantum Physics · Physics 2018-05-08 Giovanni Ramírez

Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a 2D spin lattice. Their Hamiltonian defines the groundspace by imposing an energy penalty to any nontrivial flux or charge,…

Quantum Physics · Physics 2017-12-06 Anna Komar , Olivier Landon-Cardinal

Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter. Motivated by the physics of the Kitaev quantum spin liquid [1], we study quantum circuit dynamics in…

Strongly Correlated Electrons · Physics 2022-07-08 Ali Lavasani , Zhu-Xi Luo , Sagar Vijay

In this paper, we give a generalization of Kitaev's stabilizer code based on chain complex theory of bicommutative Hopf algebras. Due to the bicommutativity, the Kitaev's stabilizer code extends to a broader class of spaces, e.g. finite…

Mathematical Physics · Physics 2021-01-08 Minkyu Kim

We consider a theory of superselection sectors for infinite quantum spin systems, describing charges that can be approximately localized in cone-like regions. The primary examples we have in mind are the anyons (or charges) in topologically…

Mathematical Physics · Physics 2020-01-20 Matthew Cha , Pieter Naaijkens , Bruno Nachtergaele

We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free…

Strongly Correlated Electrons · Physics 2010-11-23 Yue Yu

We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the…

Quantum Physics · Physics 2018-06-22 Yu-Ran Zhang , Yu Zeng , Heng Fan , J. Q. You , Franco Nori

We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models, in which the Hamiltonian is gradually simplified along a parallel…

Strongly Correlated Electrons · Physics 2011-08-17 Miguel Aguado

In the field of frustrated magnetism, Kitaev models provide a unique framework to study the phenomena of spin fractionalization and emergent lattice gauge theories in two and three spatial dimensions. Their ground states are quantum spin…

In this comprehensive study of Kitaev's abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the…

Mathematical Physics · Physics 2017-05-24 Sven Bachmann

The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local…

Strongly Correlated Electrons · Physics 2008-11-26 Eduardo Fradkin , Joel E. Moore

Topological order, reflected in long range patterns of entanglement, is quantified by the topological entanglement entropy (TEE) $\gamma$. We show that for gapped quantum spin liquids (QSL) it is possible to extract $\gamma$ using two-spin…

Strongly Correlated Electrons · Physics 2022-10-17 Shi Feng , Yanjun He , Nandini Trivedi

The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…

Strongly Correlated Electrons · Physics 2008-02-22 Miguel Aguado , Guifre Vidal