Holographic lattices, dimers, and glasses

Kachru, Shamit; Karch, Andreas; Yaida, Sho

doi:10.1103/physrevd.81.026007

Cited by 77 publications

(143 citation statements)

References 61 publications

Supporting

Mentioning

142

Contrasting

Order By: Relevance

“…It is interesting to compare our arguments with the recent results of Kachru et al [32]. They used an intersecting D-brane construction to introduce point-like impurities with spin degrees of freedom which were coupled to a background CFT.…”

mentioning

confidence: 78%

“…For each such impurity there was an asymptotic AdS 2 and an associated degeneracy of the ground state; a lattice of impurities led to a non-zero entropy density at T = 0. Thus working from their picture, it is very natural to associate AdS 2 ×R 2 with a lattice of interacting spins; with supersymmetry [32], or in a mean-field theory [17], such a model can have a non-zero entropy density. The similarity between these theories leads us to conjecture that a possible true ground state of the quantum gravity theory of the holographic metal is a spontaneously formed crystal of spins coupled to the Fermi surface of conduction electrons.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Holographic Metals and the Fractionalized Fermi Liquid

2010

View full text Add to dashboard Cite

We show that there is a close correspondence between the physical properties of holographic metals near charged black holes in anti-de Sitter (AdS) space, and the fractionalized Fermi liquid phase of the lattice Anderson model. The latter phase has a 'small' Fermi surface of conduction electrons, along with a spin liquid of local moments. This correspondence implies that certain mean-field gapless spin liquids are states of matter at non-zero density realizing the near-horizon, AdS2×R 2 physics of Reissner-Nordström black holes.There has been a flurry of recent activity [1-10] on the holographic description of metallic states of non-zero density quantum matter. The strategy is to begin with a strongly interacting conformal field theory (CFT) in the ultraviolet (UV), which has a dual description as the boundary of a theory of gravity in anti-de Sitter (AdS) space. This CFT is then perturbed by a chemical potential (µ) conjugate to a globally conserved charge, and the infrared (IR) physics is given a holographic description by the gravity theory. For large temperatures T ≫ µ, such an approach is under good control, and has produced a useful hydrodynamic description of the physics of quantum criticality [11]. Much less is understood about the low temperature limit T ≪ µ: a direct solution of the classical gravity theory yields boundary correlation functions describing a non-Fermi liquid metal [4], but the physical interpretation of this state has remained obscure. It has a non-zero entropy density as T → 0, and this raises concerns about its ultimate stability. This paper will show that there is a close parallel between the above theories of holographic metals, and a class of mean-field theories of the 'fractionalized Fermi liquid' (FFL) phase of the lattice Anderson model. The Anderson model (specified below) has been a popular description of inter-metallic transition metal or rareearth compounds: it describes itinerant conduction electrons interacting with localized resonant states representing d (or f ) orbitals. The FFL is an exotic phase of the Anderson model, demonstrated to be generically stable in Refs. [12,13]: it has a 'small' Fermi surface whose volume is determined by the density of conduction electrons alone, while the d electrons form a fractionalized spin liquid state. The FFL was also found in a large spatial dimension mean field theory by Burdin et al. [14], and is the ground state needed for a true "orbital-selective Mott transition" [15]. The FFL should be contrasted from the conventional Fermi liquid phase (FL), in which there is a 'large' Fermi surface whose volume counts both the conduction and d electrons: the FL phase is the accepted description of many 'heavy fermion' rare-earth intermetallics. However, recent experiments on YbRh 2 (Si 0.95 Ge 0.05 ) 2 have observed an unusual phase for which the FFL is an attractive candidate [16].Here, we will describe the spin liquid of the FFL by the gapless mean-field state of Sachdev and Ye [17] (SY). We will then find that physical properties of the ...

show abstract

mentioning

confidence: 78%

mentioning

confidence: 99%

Holographic Metals and the Fractionalized Fermi Liquid

2010

View full text Add to dashboard Cite

show abstract

“…5 It is straightforward to check that for the embedding at hand there is no contribution to the action coming from the WZ term.…”

Section: Action and Equations Of Motionmentioning

confidence: 99%

“…These include setups with different holographic realizations of lattices [5][6][7][8][9][10][11][12] through periodically space-dependent sources, and also setups implementing disordered sources [13][14][15][16]. Moreover, a lattice realization where PDEs are avoided, which goes under the name of Q-lattices given its resemblance to the construction of Q-balls [17], was introduced in [18] and further explored in [19,20].…”

Section: Jhep08(2015)146mentioning

confidence: 99%

Holographic charge localization at brane intersections

Araujo

Areán

Erdmenger

et al. 2015

J. High Energ. Phys.

View full text Add to dashboard Cite

Using gauge/gravity duality, we investigate charge localization near an interface in a strongly coupled system. For this purpose we consider a top-down holographic model and determine its conductivities. Our model corresponds to a holographic interface which localizes charge around a (1+1)-dimensional defect in a (2+1)-dimensional system. The setup consists of a D3/D5 intersection at finite temperature and charge density. We work in the probe limit, and consider massive embeddings of a D5-brane where the mass depends on one of the field theory spatial directions, with a profile interpolating between a negative and a positive value. We compute the conductivity in the direction parallel and perpendicular to the interface. For the latter case we are able to express the DC conductivity as a function of background horizon data. At the interface, the DC conductivity in the parallel direction is enhanced up to five times with respect to that in the orthogonal one. We study the implications of broken translation invariance for the AC and DC conductivities.

show abstract

“…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%

Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

View full text Add to dashboard Cite

Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).Keywords: strongly correlated systems, holographic correspondence, transport theory, strange metals, analogue gravity PACS: 71.27.+a Condensed matter holography: the promiseAmong the outstanding grand problems in condensed matter physics is that of a deeper understanding and classification of the so-called 'strange metals' or compressible non-Fermi liquid (NFL) states of the strongly interacting systems. However, despite all the effort and a plethora of the important and nontrivial results obtained with the use of the traditional techniques, this program still remains far from completion.As an alternate approach, over the past decade there have been numerous attempts inspired by the hypothetical idea of holographic correspondence which originated from string/gravity/high energy theory (where it is known under the acronym AdS/ CFT) to adapt its main concepts to various condensed matter (or, even more generally, quantum manybody) systems at finite densities and temperatures [1][2][3][4][5][6][7].In its original context, the bona fide holographic principle postulates that certain d + 1-dimensional ('boundary') quantum field theories (e. g. the maximally supersymmetric SU(N) gauge theory) may allow for a dual description in terms of a string theory which, upon a proper compactification, amounts to a certain d + 2-dimensional ('bulk') supergravity. Moreover, in the strong coupling limit (characterized in terms of the t'Hooft coupling constant λ = g 2 N >> 1) and for a large rank N > > 1 of the gauge symmetry group, the bulk description can be further reduced down to a weakly fluctuating gravity model which can even be treated semiclassically at the lowest (0th) order of the underlying 1/N-expansion.In the practical applications of the holographic conjecture, the partition function of a strongly interacting boundary theory with the Lagrangian L(ϕ a ) would then be approximated by a saddle-point (classical) value of the bulk action described by the Lagrangian L(g μν ,…) which includes gravity and other fields dual to their boundary counterparts [1][2][3][4][5][6][7][8] (1) evaluated with the use of a fixed background metric ,while any quantum corrections would usually be neglected by invoking the small parameter 1/N.

show abstract

Holographic lattices, dimers, and glasses

Cited by 77 publications

References 61 publications

Holographic Metals and the Fractionalized Fermi Liquid

Holographic Metals and the Fractionalized Fermi Liquid

Holographic charge localization at brane intersections

Demystifying the holographic mystique: A critical review

Contact Info

Product

Resources

About