2016
DOI: 10.1103/physrevb.93.035112
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Exact holographic mapping in free fermion systems

Abstract: In this paper, we perform a detailed analysis of the Exact Holographic Mapping first introduced in arXiv:1309.6282, which was proposed as an explicit example of holographic duality between quantum many-body systems and gravitational theories. We obtain analytic results for free fermion systems that not only confirm previous numerical results, but also elucidate the exact relationships between the various physical properties of the bulk and boundary systems. These analytic results allow us to study the asymptot… Show more

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Cited by 43 publications
(88 citation statements)
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“…25 The strong triangle inequality (4.6) also implies |x+x| p ≤ |x| p , which violates the 23 Note that the original triangle inequality is trivially satisfied by the p-adic norm: |x + y|p ≤ |x|p + |y|p. 24 The Euclidean norm |x| and the p-adic norm |x|p are the only possible norms to complete the rational field Q (giving R and Qp, respectively), as already shown by Ostrowski in 1919 [47]. 25 Note that in contrast to the decimal expansion for the real number x ∈ R, for a p-adic number xp ∈ Qp,…”
Section: The Field Q P Of P-adic Numbersmentioning
confidence: 90%
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“…25 The strong triangle inequality (4.6) also implies |x+x| p ≤ |x| p , which violates the 23 Note that the original triangle inequality is trivially satisfied by the p-adic norm: |x + y|p ≤ |x|p + |y|p. 24 The Euclidean norm |x| and the p-adic norm |x|p are the only possible norms to complete the rational field Q (giving R and Qp, respectively), as already shown by Ostrowski in 1919 [47]. 25 Note that in contrast to the decimal expansion for the real number x ∈ R, for a p-adic number xp ∈ Qp,…”
Section: The Field Q P Of P-adic Numbersmentioning
confidence: 90%
“…We thus see that the rational field Q can have infinitely many different norms: the Euclidean norm |x| together with the p-adic norms |x| p for each prime p. 24 The real field R is only one possible extension of Q, using the Euclidean norm |x|. Now, for each prime p, we can have a different extension of Q using the p-adic norms |x| p .…”
Section: The Field Q P Of P-adic Numbersmentioning
confidence: 99%
See 1 more Smart Citation
“…On the other hand, there exist, of course, important ongoing efforts towards, both, constructing various 'top-down' holographic models [9][10][11][12][13] as well as trying to derive holography from the already known concepts such as a renormalization procedure on the information-related tensor networks [14][15][16][17][18][19][20][21][22][23][24]. However, the former approach formulated in terms of such objects as D-branes remains to be rather exotic and somewhat hard to connect to from the CMT perspective, whereas the latter one (which, in practice, amounts to a massive use of the Stratonovich and Trotter transformations combined with numerical solutions of the resulting flow equations of the functional RG-type) has yet to deliver a well-defined bulk geometry, other than the basic AdS with the dynamical z = 1 (or its Lifshitz modification with z = 2), that would be reminiscent of those metrics which are extensively utilized in the 'bottom-up' studies (see below).…”
Section: Condensed Matter Holography: the Promisementioning
confidence: 99%
“…In higher dimensions, the Crofton's formula can be generalized [37], 15) where σ n denotes the volume (area/length) of an n-dimensional object and O n is the area of unit n-sphere…”
Section: )mentioning
confidence: 99%