From Entanglement Generated Dynamics to the Gravitational Anomaly and Chiral Central Charge

Fan, Ruihua

doi:10.1103/physrevlett.129.260403

Cited by 14 publications

(10 citation statements)

References 30 publications

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“…However, if one wants to extract ζ n , one also needs to know about the chiral central charge c − , which could be obtained from either some prior knowledge about the topological order, or the momentum polarization [23,24], or certain entanglement measures [6,7,9,10]. Our numerical algorithm can easily reproduce the momentum polarization by taking the large n limit, though the physics is completely different as explained in the main text.…”

Section: Extracting Higher Central Charge Of the ν = 1/2 Bosonic Laug...mentioning

confidence: 99%

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Extracting higher central charge from a single wave function

Kobayashi¹,

Wang²,

Soejima³

et al. 2023

Preprint

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A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c− is vanishing. Recently, it is discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c− to gapping out the edge. In this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wavefunction of the topologically ordered state. This allows us to extract the higher central charge from a single wavefunction, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)2 and Ising topological order respectively. The letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c−. We also point out that the expectation values of the partial rotation on a single wavefunction put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis type theorems.

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Section: Extracting Higher Central Charge Of the ν = 1/2 Bosonic Laug...mentioning

confidence: 99%

“…Even in the absence of charge conservation, systems with nonzero chiral central charge, which signals nonzero thermal Hall conductance, has gapless edge modes [3]. We have a good theoretical understanding of these quantities by way of coarsegrained Chern-Simons theory, and we can extract them from microscopic wavefunctions [4][5][6][7][8][9][10][11][12][13].…”

mentioning

confidence: 99%

Extracting higher central charge from a single wave function

Kobayashi¹,

Wang²,

Soejima³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular, it can not distinguish abelian and nonabelian TOs which have very different properties and applications. There have been efforts to extract other universal quantities of a TO, such as the chiral central charge either from edge thermal transport [17][18][19] or the bulk wave function [20][21][22][23] , the higher central charge 24 , and the many-body Chern number [25][26][27] .…”

mentioning

confidence: 99%

Anyon quantum dimensions from an arbitrary ground state wave function

Liu

2024

Nat Commun

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Realizing topological orders and topological quantum computation is a central task of modern physics. An important but notoriously hard question in this endeavor is how to diagnose topological orders that lack conventional order parameters. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to detect nontrivial topological order from a ground state wave function, but is far from enough for fully determining the topological order. In this work, we take a key step further in this direction: We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. The choice of the space manifold and the ground state is arbitrary. This protocol is both validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.

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“…The answer is no. It is known that, if the CCC is non-zero, we cannot define the Schmidt decomposition or the reduced density matrix[71,72], and hence the entanglement entropy cannot be defined properly either.…”

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confidence: 99%

AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles

Kusuki

Wei

2023

J. High Energ. Phys.

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We initiate a conformal bootstrap program to study AdS3/BCFT2 with heavy excitations. We start by solving the bootstrap equations associated with two-point functions of scalar/non-scalar primaries under the assumption that one-point functions vanish. These correspond to gravity with a brane and a non-spinning/spinning particle where the brane and the particle do not intersect with each other. From the bootstrap equations, we obtain the energy spectrum and the modified black hole threshold. We then carefully analyze the gravity duals and find the results perfectly match the BCFT analysis. In particular, brane self-intersections, which are usually considered to be problematic, are nicely avoided by the black hole formation. Despite the assumption to solve the bootstrap equations, one-point functions of scalar primaries can be non-zero in general. We construct the holographic dual for a non-vanishing one-point function, in which the heavy particle can end on the brane, by holographically computing the Rényi entropy in AdS/BCFT. As a bonus, we find a refined formula for the holographic Rényi entropy, which appears to be crucial to correctly reproduce the boundary entropy term. On the other hand, we explain why one-point functions of non-scalar primaries always vanish from the gravity dual. The non-sensitivity of the solution for the bootstrap equation to the boundary entropy helps us to construct gravity duals with negative tension branes. We also find a holographic dual of boundary primaries.

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From Entanglement Generated Dynamics to the Gravitational Anomaly and Chiral Central Charge

Cited by 14 publications

References 30 publications

Extracting higher central charge from a single wave function

Extracting higher central charge from a single wave function

Anyon quantum dimensions from an arbitrary ground state wave function

AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles

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