Non-local order parameters and quantum entanglement for fermionic topological field theories

Inamura, Kansei; Kobayashi, Ryohei; Ryu, Shinsei

doi:10.1007/jhep01(2020)121

Cited by 8 publications

(7 citation statements)

References 57 publications

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“…5 In the case of antiunitary symmetries it requires, for example, learning how to define spin TQFTs on unoriented manifolds, which is an open problem. Numerous interesting partial results have been obtained, however [18,[36][37][38][39][40][41][42][43]. 6 One could also study the reduction of the anomaly class on more general manifolds, potentially detecting more anomalies.…”

Section: Jhep11(2021)142mentioning

confidence: 99%

Global anomalies on the Hilbert space

Delmastro

Gaiotto

Gomis

2021

J. High Energ. Phys.

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We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology “layers” that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2 + 1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

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Section: Jhep11(2021)142mentioning

confidence: 99%

Global anomalies on the Hilbert space

Delmastro

Gaiotto

Gomis

2021

J. High Energ. Phys.

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“…The sign factor turns out to be an essential difference between the bosonic PT (which is applied to spin chains, harmonic chains, qubits, etc.) and the fermionic PT, especially when it comes to partition functions of fermionic systems with a fixed spin structure [95,96]. Although the fermionic PT can be derived as the only definition consis-tent with operator algebras in fermionic systems (see for instance Ref.…”

Section: (I)mentioning

confidence: 99%

Anyonic Partial Transpose I: Quantum Information Aspects

Shapourian¹,

Mong²,

Ryu³

2020

Preprint

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A basic diagnostic of entanglement in mixed quantum states is known as the partial transpose and the corresponding entanglement measure is called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the partial transpose to fermionic systems remained a technical challenge until recently when a new definition that accounts for the Fermi statistics was put forward. In this paper, we propose a way to generalize the partial transpose to anyons with (non-Abelian) fractional statistics based on the apparent similarity between the partial transpose and the braiding operation. We then define the anyonic version of the logarithmic negativity and show that it satisfies the standard requirements such as monotonicity to be an entanglement measure. In particular, we elucidate the properties of the anyonic logarithmic negativity by computing it for a toy density matrix of a pair of anyons within various categories. We conjecture that the subspace of states with a vanishing logarithmic negativity is a set of measure zero in the entire space of anyonic states, in contrast with the ordinary qubit systems where this subspace occupies a finite volume. We prove this conjecture for multiplicity-free categories.

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“…The negativity spectrum has been studied in many-body quantum systems -see e.g., refs. [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Negativity spectra in random tensor networks and holography

Kudler-Flam

Narovlansky

Ryu

2022

J. High Energ. Phys.

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Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and “phase” of entanglement. For pure states, it is simply determined by the entanglement spectrum. We use a diagrammatic method complemented by a modification of the Ford-Fulkerson algorithm to find the negativity spectrum in general random tensor networks with large bond dimensions. In holography, these describe the entanglement of fixed-area states. It was found that many fixed-area states have a negativity spectrum given by a semi-circle. More generally, we find new negativity spectra that appear in random tensor networks, as well as in phase transitions in holographic states, wormholes, and holographic states with bulk matter. The smallest random tensor network is the same as a micro-canonical version of Jackiw-Teitelboim (JT) gravity decorated with end-of-the-world branes. We consider the semi-classical negativity of Hawking radiation and find that contributions from islands should be included. We verify this in the JT gravity model, showing the Euclidean wormhole origin of these contributions.

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Non-local order parameters and quantum entanglement for fermionic topological field theories

Cited by 8 publications

References 57 publications

Global anomalies on the Hilbert space

Global anomalies on the Hilbert space

Anyonic Partial Transpose I: Quantum Information Aspects

Negativity spectra in random tensor networks and holography

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