Related papers: Topological entanglement entropy to identify topol…
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…
We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase…
We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer…
A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid, 110405]. It was argued that in a topological…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
We find that the topological phase transition in a chiral ladder is characterized by dramatic signatures in many body entanglement entropy between the legs, close to half-filling. The value of entanglement entropy for various fillings close…
"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 magnetism, skyrmions correspond to classical three-dimensional spin textures characterized by a topological invariant that keeps track of the winding of the magnetization in real space, a property that cannot be easily generalized to the…
These lecture notes on entanglement in topological systems are part of the 48th IFF Spring School 2017 on Topological Matter: Topological Insulators, Skyrmions and Majoranas at the Forschungszentrum Juelich, Germany. They cover a short…
Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally…
We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from…
We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Quantum Spin Liquids (QSLs) are phases of interacting spins that do not order even at the absolute zero temperature, making it impossible to characterize them by a local order parameter. In this article, we review the unique view provided…
We study the entropy of chiral 2+1-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition…
Topologically stable structures include vortices in a wide variety of matter, such as skyrmions in ferro- and antiferromagnets, and hedgehog point defects in liquid crystals and ferromagnets. These are characterized by integer-valued…
Chiral magnets, characterized by inhomogeneous magnetic moment arrangements, have attracted significant attention recently due to their topological orders, such as magnetic skyrmion lattices and chiral soliton lattices. In this work, we…
We study the entanglement structure of Abelian topological order described by $p$-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface…
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…