Thermal geometry from CFT at finite temperature

Gan, Wen-Cong; Shu, Fu-Wen; Wu, Meng-He

doi:10.1016/j.physletb.2016.07.073

Cited by 10 publications

(7 citation statements)

References 41 publications

(64 reference statements)

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“…Another important future problem which is of close correlation is to find which factor determines the emergent spacetime to be thermal AdS or BTZ black hole, or equivalently, the Hawking-Page phase transition. In our previous work [12] we have found a cMERA description of the Hawking-Page phase transition in the framework of the truncated MERA.…”

Section: Discussionmentioning

confidence: 99%

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Emergent geometry, thermal CFT and surface/state correspondence

Gan

Shu

2017

Physics Letters B

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We study a conjectured correspondence between any codimension two convex surface and a quantum state (SS-duality for short). By generalizing thermofield double formalism to continuum version of the multi-scale entanglement renormalization ansatz (cMERA) and using the SS-duality, we show that thermal geometries naturally emerge as a result of hidden quantum entanglement between boundary CFTs. We therefore propose a general framework to emerge the thermal geometry from CFT at finite temperature. As an example, the case of $2d$ CFT is considered. We calculate its information metric and show that it is either BTZ black hole or thermal AdS as expected.Comment: 13 pages, 3 figure

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Section: Discussionmentioning

confidence: 99%

“…We often call it the truncated MERA [11]. In our previous work [12], we discussed the emergent thermal geometry by generalizing the truncated MERA to continuous one.…”

Section: Introductionmentioning

confidence: 99%

Emergent geometry, thermal CFT and surface/state correspondence

Gan

Shu

2017

Physics Letters B

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“…A TN operator is regarded as a mapping from the bra to the ket Hilbert space. Many algorithms explicitly employ the TN operator form, including the matrix product operator (MPO) for representing 1D many-body operators and mixed states, and for simulating 1D systems in and out of equilibrium [186,187,188,189,190,191,192,193,194,195,196], tensor product operator (also called projected entangled pair operators) in for higher-systems [140,141,143,197,198,199,200,201,202,203,204,205,206], and multiscale entangled renormalization ansatz [207,208,209].…”

Section: Tensor Network States In Two Dimensionsmentioning

confidence: 99%

Tensor Network Contractions

Ran

Tirrito

Peng

et al. 2020

Lecture Notes in Physics

105

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PrefaceTensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum information science, statistical physics, and so on. In this lecture notes, we focus on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems. Starting from basic concepts and definitions, we first explain the relations between TN and physical problems, including the TN representations of classical partition functions, quantum many-body states (by matrix product state, tree TN, and projected entangled pair state), time evolution simulations, etc. These problems, which are challenging to solve, can be transformed to TN contraction problems. We present then several paradigm algorithms based on the ideas of the numerical renormalization group and/or boundary states, including density matrix renormalization group, time-evolving block decimation, coarsegraining/corner tensor renormalization group, and several distinguished variational algorithms. Finally, we revisit the TN approaches from the perspective of multilinear algebra (also known as tensor algebra or tensor decompositions) and quantum simulation. Despite the apparent differences in the ideas and strategies of different TN algorithms, we aim at revealing the underlying relations and resemblances in order to present a systematic picture to understand the TN contraction approaches. v AcknowledgementsWe are indebted to

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“…The tensor-network interpratation [5] of the RT formula provides further evidence. Especially, it was argued that quantum entanglement is fundamental in building geometries of holographic spacetime [6][7][8]. However, just as pointed out by Susskind [10], "entanglement is not enough", and it is natural to find other quantum information quantities which can be used in studying holography.…”

Section: Introductionmentioning

confidence: 99%

Holographic complexity: A tool to probe the property of reduced fidelity susceptibility

Gan

Shu

2017

Phys. Rev. D

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Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge for present theory and experiments. In this paper, we investigate a recent conjectured connection between reduced fidelity susceptibility and holographic complexity (the RFS/HC duality for short). We give a quantitative proof of the duality by performing both holographic and field theoretical computations. In addition, holographic complexity in AdS 2+1 are explored and several important properties are obtained. These properties allow us, via the RFS/HC duality, to obtain a set of remarkable identities of the reduced fidelity susceptibility, which may have significant implications for our understanding of the reduced fidelity susceptibility. Moreover, utilizing these properties and the recent proposed diagnostic tool based on the fidelity susceptibility, experimental verification of the RFS/HC duality becomes possible.

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Thermal geometry from CFT at finite temperature

Cited by 10 publications

References 41 publications

Emergent geometry, thermal CFT and surface/state correspondence

Emergent geometry, thermal CFT and surface/state correspondence

Tensor Network Contractions

Holographic complexity: A tool to probe the property of reduced fidelity susceptibility

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