arXiv subjects

Robert G. Leigh

Publications and source records attributed to Robert G. Leigh.

At least 73 records · Page 4Linked to original sources

arXiv2011

Torsional Response and Dissipationless Viscosity in Topological Insulators

We consider the visco-elastic response of the electronic degrees of freedom in 2D and 3D topological insulators (TI). Our primary focus is on the 2D Chern insulator which exhibits a bulk dissipationless viscosity analogous to the quantum Hall viscosity predicted in integer and fractional quantum Hall states. We show that the dissipationless viscosity is the response of a TI to torsional deformations of the underlying lattice geometry. The visco-elastic response also indicates that crystal dislocations in Chern insulators will carry momentum density. We briefly discuss generalizations to 3D which imply that time-reversal invariant TI's will exhibit a quantum Hall viscosity on their surfaces.

cond-mat.mes-hall↗

arXiv2010

Fermions and Type IIB Supergravity On Squashed Sasaki-Einstein Manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N=4 gauged supergravity in $d=5$, coupled to two vector multiplets. We compute fermion masses by linearizing around two $AdS_{5}$ vacua of the theory: one that breaks N=4 down to N=2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under a U(1) subgroup of the $R$-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.

hep-th↗

arXiv2010

Fermions and D=11 Supergravity On Squashed Sasaki-Einstein Manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of D=11 supergravity compactified on squashed seven-dimensional Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have $(2+1)$-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which most notably include charged scalar and form fields. We demonstrate that our results are consistent with the expected supersymmetric structure of the lower dimensional theory, and apply them to a specific example which is relevant to the study of $(2+1)$-dimensional holographic superconductors.

hep-th↗

arXiv2010

Dynamical Gap and Cuprate-like Physics from Holography

We study the properties of fermion correlators in a boundary theory dual to the Reissner-Nordström AdS_{d+1} background in the presence of a bulk dipole (Pauli) interaction term with strength p. We show that by simply changing the value of the parameter p we can tune continuously from a Fermi liquid (small p), to a marginal Fermi liquid behavior at a critical value of p, to a generic non-Fermi liquid at intermediate values of p, and finally to a Mott insulator at large values of the bulk Pauli coupling. As all of these phases are seen in the cuprate phase diagram, the holographic model we study has the key elements of the strong coupling physics typified by Mott systems. In addition, we extend our analysis to finite temperature and show that the Mott gap closes. Of particular interest is that it closes when the ratio of the gap to the critical temperature is of the order of ten. This behavior is very much similar to that observed in the classic Mott insulator VO_2. We then analyze the non-analyticities of the boundary theory fermion correlators for generic values of frequency and momentum by calculating the quasi-normal modes of the bulk fermions. Not surprisingly, we find no evidence for the dipole interaction inducing an instability in the boundary theory. Finally, we briefly consider the introduction of superconducting condensates, and find that in that case, the fermion gap is driven by scalar-fermion couplings rather than by the Pauli coupling.

hep-th↗

arXiv2010

Aging and Holography

Aging phenomena are examples of `non-equilibrium criticality' and can be exemplified by systems with Galilean and scaling symmetries but no time translation invariance. We realize aging holographically using a deformation of a non-relativistic version of gauge/gravity duality. Correlation functions of scalar operators are computed using holographic real-time techniques, and agree with field theory expectations. At least in this setup, general aging phenomena are reproduced holographically by complexifying the bulk space-time geometry, even in Lorentzian signature.

hep-th↗

arXiv2010

Holography and the sound of criticality

Using gauge/gravity duality techniques, we discuss the sound-channel retarded correlators of vector and tensor conserved currents in a class of $(2+1)$-dimensional strongly-coupled field theories at zero temperature and finite charge density, assumed to be holographically dual to the extremal Reissner-Nordström AdS$_4$ black hole. Using a combination of analytical and numerical methods, we determine the quasinormal mode spectrum at finite momentum for the coupled gravitational and electromagnetic perturbations, and discuss the appropriate choice of gauge-invariant variables (master fields) in order for the black hole quasinormal frequencies to reproduce the field theory spectrum. We discuss the role of the near horizon AdS$_{2}$ geometry in determining the low-frequency behavior of retarded correlators in the boundary theory, and comment on the emergence of criticality in the IR. In addition, we establish the existence of a sound mode at zero temperature and compute the speed of sound and sound attenuation constant numerically, obtaining a result consistent with the expectations from the zero temperature limit of hydrodynamics. The dispersion relation of higher resonances is also investigated.

hep-th↗

arXiv2010

Gauge Fields, Membranes and Subdeterminant Vector Models

We present a class of classically marginal N-vector models in d=4 and d=3, whose scalar potentials can be written as subdeterminants of symmetric matrices. The d=3 case is a generalization of the scalar Bagger-Lambert-Gustavsson (BLG) model. Using the Hubbard-Stratonovich transformation we calculate their effective potentials which exhibit intriguing large-N scaling behaviors. We comment on the relevance of our models to strings, membranes and also to a class of novel spin systems that are based on ternary commutation relations.

hep-th↗

arXiv2010

Shear Modes, Criticality and Extremal Black Holes

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.

hep-th↗

arXiv2009

Fermions and the Sch/nrCFT Correspondence

We consider the problem of Dirac fermions propagating on a spacetime of Schrödinger isometry and the associated boundary Euclidean two-point function of fermionic scaling operators of the holographic dual non-relativistic conformal theory. Paying careful attention to the representations of the Schrödinger algebra that appear in this problem, we show carefully how the on-shell action is constructed and how the boundary theory may be renormalized consistently by the inclusion of appropriate Galilean invariant boundary counterterms.

hep-th↗

arXiv2009

Transport Coefficients at Zero Temperature from Extremal Black Holes

Using the AdS/CFT correspondence we study transport coefficients of a strongly-coupled (2 +1)-dimensional field theory at {\it zero} temperature and finite charge density. The field theory under consideration is dual to the extremal Reissner-Nordstrom AdS_4 black hole in the bulk. We show that, like the cases of scalar and spinor operators studied in \cite{Faulkner:2009wj}, the correlators of charge (vector) current and energy-momentum (tensor) operators exhibit scaling behavior at low frequency. The existence of such low frequency behavior is related to the fact that the near-horizon geometry of the extremal black hole background has an AdS_2 factor. We carefully calculate the shear viscosity (at zero temperature) and show that the ratio of the shear viscosity to the entropy density takes the value of 1/4π. Because of the AdS_2 factor, we argue that this result stays the same for all d-dimensional boundary field theories dual to the extremal Reissner-Nordstrom AdS_{d+1} black holes. Also, we compute the charge conductivity at zero temperature. The limiting behavior of the conductivity for small frequencies is also attributed to the near horizon AdS_2 factor and is argued to hold regardless of the dimension of the zero-temperature boundary field theory. Finally, using the extremal dyonic AdS_4 black hole as the background, we extract the conductivity in the presence of a constant magnetic field.

hep-th↗

arXiv2009

Real-Time Correlators and Non-Relativistic Holography

We consider Lorentzian correlation functions in theories with non-relativistic Schrodinger symmetry. We employ the method developed by Skenderis and van Rees in which the contour in complex time defining a given correlation function is associated holographically with the gluing together of Euclidean and Lorentzian patches of spacetimes. This formalism extends appropriately to geometries with Schrodinger isometry.

hep-th↗

arXiv2009

Mottness in High-Temperature Copper-Oxide Superconductors

The standard theory of metals, Fermi liquid theory, hinges on the key assumption that although the electrons interact, the low-energy excitation spectrum stands in a one-to-one correspondence with that of a non-interacting system. In the normal state of the copper-oxide high-temperature superconductors, drastic deviations from the Fermi liquid picture obtain, highlighted by a pseudogap, broad spectral features and $T-$ linear resistivity. This article focuses on the series of experiments on the copper-oxide superconductors which reveal that the number of low-energy addition states per electron per spin exceeds unity, in direct violation of the key Fermi liquid tenet. These experiments point to new degrees of freedom, not made out of the elemental excitations, as the key mechanism by which Fermi liquid theory breaks down in the cuprates. A recent theoretical advance which permits an explicit integration of the high energy scale in the standard model for the cuprates reveals the source of the new dynamical degrees of freedom at low energies, a charge 2e bosonic field which has nothing to do with pairing but rather represents the mixing with the high energy scales. We demonstrate explicitly that at half-filling, this new degree of freedom provides a dynamical mechanism for the generation of the charge gap, antiferromagnetism in the insulating phase and explains many of the anomalies in the normal state of the cuprates.

cond-mat.str-el↗

arXiv2009

Transversely-intersecting D-branes at finite temperature and chiral phase transition

We consider Sakai-Sugimoto like models consisting of Dq-Dp-anti-Dp-branes where flavor Dp and anti-Dp-branes transversely intersect color Dq-branes along two (r+1)-dimensional subspaces. For some values of p and q, the theory of intersections dynamically breaks non-Abelian chiral symmetry which is holographically realized as a smooth connection of the flavor branes at some point in the bulk of the geometry created by Dq-branes. We analyze the system at finite temperature and map out different phases of the theory representing chiral symmetry breaking and restoration. For q<5 we find that, unlike the zero-temperature case, there exist two branches of smoothly-connected solutions for the flavor branes, one getting very close to the horizon of the background and the other staying farther away from it. At low temperatures, the solution which stays farther away from the horizon determines the vacuum. For background D5 and D6-branes we find that the flavor branes, like the zero temperature case, show subtle behavior whose dual gauge theory interpretation is not clear. We conclude with some comments on how chiral phase transition in these models can be seen from their open string tachyon dynamics.

hep-th↗

arXiv2008

Open Wilson Lines and Chiral Condensates in Thermal Holographic QCD

We investigate various aspects of a proposal by Aharony and Kutasov arXiv:0803.3547 [hep-th] for the gravity dual of an open Wilson line in the Sakai-Sugimoto model or its non-compact version. In particular, we use their proposal to determine the effect of finite temperature, as well as background electric and magnetic fields, on the chiral symmetry breaking order parameter. We also generalize their prescription to more complicated worldsheets and identify the operators dual to such worldsheets.

hep-th↗

arXiv2008

Torsion and the Gravity Dual of Parity Symmetry Breaking in AdS4/CFT3 Holography

We study four dimensional gravity with a negative cosmological constant deformed by the Nieh-Yan torsional topological invariant with a spacetime-dependent coefficient. We find an exact solution of the Euclidean system, which we call the torsion vortex, having two asymptotic AdS4 regimes supported by a pseudoscalar with a kink profile. We propose that the torsion vortex is the holographic dual of a three dimensional system that exhibits distinct parity breaking vacua. The torsion vortex represents a (holographic) transition between these distinct vacua. We expect that from the boundary point of view, the torsion vortex represents a `domain wall' between the two distinct vacua. From a bulk point of view, we point out an intriguing identification of the parameters of the torsion vortex with those of an Abrikosov vortex in a Type I superconductor. Following the analogy, we find that external Kalb-Ramond flux then appears to support bubbles of flat spacetime within an asymptotically AdS geometry.

hep-th↗

arXiv2008

Breakdown of Fermi Liquid Theory in Doped Mott Insulators by Dynamical Spectral Weight Transfer

We show that doped Mott insulators exhibit a collective degree of freedom, not made out of the elemental excitations, because the number of single-particle addition states at low energy per electron per spin is greater than one. The presence of such a collective degree of freedom which is not a consequence of proximity to a phase transition is a consequence of dynamical spectral weight transfer from high to low energies. This physics is captured by the charge $2e$ boson that emerges by explicitly integrating out the high-energy scale in the Hubbard model. The charge $2e$ boson binds to a hole, thereby mediating new charge $e$ states at low energy. It is the presence of such charge $e$ states which have no counterpart in the non-interacting system that provides the general mechanism for the breakdown of Fermi liquid theory in doped Mott insulators. The relationship between the charge $2e$ boson formulation and the standard perturbative treatment is explained.

cond-mat.str-el↗

arXiv2008

Hidden Charge 2e Boson: Experimental Consequences for Doped Mott Insulators

We show here that many of the normal state properties of the cuprates can result from the new charge 2e bosonic field which we have recently (Phys. Rev. Lett. {\bf 99}, 46404 (2007) and Phys. Rev. B 77, 014512 (2008)) shown to exist in the exact low-energy theory of a doped Mott insulator. In particular, the 1) mid-infrared band including the non-vanishing of the restricted f-sum rule in the Mott insulator, 2) the $T^2$ contribution to the thermal conductivity, 3) the pseudogap, 4) the bifurcation of the electron spectrum below the chemical potential as recently seen in angle-resolved photoemission, 5) insulating behaviour away from half-filling, 6) the high and low-energy kinks in the electron dispersion and 7) T-linear resistivity all derive from the charge 2e bosonic field. We also calculate the inverse dielectric function and show that it possesses a sharp quasiparticle peak and a broad particle-hole continuum. The sharp peak is mediated by a new charge e composite excitation formed from the binding of a charge 2e boson and a hole and represents a distinctly new prediction of this theory. It is this feature that is responsible for dynamical part of the spectral weight transferred across the Mott gap. We propose that electron energy loss spectroscopy at finite momentum and frequency can be used to probe the existence of such a sharp feature.

cond-mat.str-el↗

arXiv2008

Exact Integration of the High Energy Scale in Doped Mott Insulators

We expand on our earlier work (cond-mat/0612130, Phys. Rev. Lett. {\bf 99}, 46404 (2007)) in which we constructed the exact low-energy theory of a doped Mott insulator by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low-energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular a new charge $\pm 2e$ bosonic field emerges at low energies that is not made out of elemental excitations. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green function vanishes. In addition, the interactions with the bosonic fields defeat the artificial local SU(2) symmetry that is present in the Heisenberg model. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. Finally, we show that as a result of the bosonic degree of freedom, the electron at low energies is in a linear superposition of two excitations--one arising from the standard projection into the low-energy sector and the other from the binding of a hole and the boson.

cond-mat.str-el↗