Emergent geometry, thermal CFT and surface/state correspondence

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

doi:10.1016/j.physletb.2017.07.011

Cited by 4 publications

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“…Demonstrating a way of describing points in the bulk AdS as states on the surface CFT, as well as demonstrating the diffeomorphic symmetry of the AdS space[79]. Others (W.-C. Gan, F.-S. Shu, and M.-H. Wu) later extended these ideas to thermal cMERA[80].…”

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A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

McMahon¹

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Modelling strongly correlated systems is an incredibly hard problem, but a very fruitful one when achieved. The main reason for its difficulty is that perturbation theory approaches do not work for certain interesting coupling regimes. However it is believed that a holographic duality would map models with strong coupling strengths into weakly coupled bulk regimes where our current tools do work. Interest in applications to condensed matter systems has been growing throughout the past decade Though questions remain about how to do it and if the duality is valid in a relevant regime.

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A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

McMahon¹

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Thermal geometry from CFT at finite temperature

Gan

Shu

2016

Physics Letters B

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We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of $2d$ CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking-Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.Comment: 11 pages, 2 figure

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Generalized exact holographic mapping with wavelets

Lee

2017

Phys. Rev. B

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The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N-dimensional lattice system to a N+1-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis-specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high pass wavelet filter is revealed to be proportional to the radius of the dual Anti deSitter (AdS) space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.arXiv:1609.06241v3 [cond-mat.other]

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Emergent geometry, thermal CFT and surface/state correspondence

Cited by 4 publications

References 54 publications

A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

Thermal geometry from CFT at finite temperature

Generalized exact holographic mapping with wavelets

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