arXiv subjects

Hong Liu

Publications and source records attributed to Hong Liu.

At least 505 records · Page 28Linked to original sources

arXiv2011

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.

hep-th↗

arXiv2011

Impact of heterogenous prior beliefs and disclosed insider trades

In this paper, we present a multi-period trading model by assuming that traders face not only asymmetric information but also heterogenous prior beliefs, under the requirement that the insider publicly disclose his stock trades after the fact. We show that there is an equilibrium in which the irrational insider camouflages his trades with a noise component so that his private information is revealed slowly and linearly whenever he is overconfident or underconfident. We also investigate the relationship between the heterogeneous beliefs and the trade intensity in the presence of trade disclosure, and show that the weights on asymmetric information and heterogeneous prior beliefs are opposite in sign and they change alternatively in the next period. Under the requirement of disclosure, the irrational insider trades more aggressively and leads to smaller market depth. Moreover, the co-existence of "public disclosure requirement" and "heterogeneous prior beliefs" leads to the fluctuant multi-period expected profits and a larger total expected trading volume which is positively related to the degree of heterogeneity. More importantly, even public disclosure may lead to negative profits of the irrational insider's in some periods, inside trading remains profitable from the whole trading period.

q-fin.TR↗

arXiv2011

Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

We formulate a holographic Wilsonian renormalization group flow for strongly coupled systems with a gravity dual, motivated by the need to extract efficiently low energy behavior of such systems. Starting with field theories defined on a cut-off surface in a bulk spacetime, we propose that integrating out high energy modes in the field theory should correspond to integrating out a part of the bulk geometry. We describe how to carry out this procedure in practice in the classical gravity approximation using examples of scalar and vector fields. By integrating out bulk degrees of freedom all the way to a black hole horizon, this formulation defines a refined version of the black hole membrane paradigm. Furthermore, it also provides a derivation of the semi-holographic description of low energy physics.

hep-th↗

arXiv2011

Dominating Sets in Triangulations on Surfaces

A dominating set D of a graph G is a set such that each vertex v of G is either in the set or adjacent to a vertex in the set. Matheson and Tarjan (1996) proved that any n-vertex plane triangulation has a dominating set of size at most n/3, and conjectured a bound of n/4 for n sufficiently large. King and Pelsmajer recently proved this for graphs with maximum degree at most 6. Plummer and Zha (2009) and Honjo, Kawarabayashi, and Nakamoto (2009) extended the n/3 bound to triangulations on surfaces. We prove two related results: (i) There is a constant c such that any n-vertex plane triangulation with maximum degree at most 6 has a dominating set of size at most n/6 + c. (ii) For any surface S, nonnegative t, and epsilon > 0, there exists C such that for any n-vertex triangulation on S with at most t vertices of degree other than 6, there is a dominating set of size at most n(1/6 + epsilon) + C. As part of the proof, we also show that any n-vertex triangulation of a non-orientable surface has a non-contractible cycle of length at most 2sqrt(n). Albertson and Hutchinson (1986) proved that for n-vertex triangulation of an orientable surface other than a sphere has a non-contractible cycle of length sqrt(2n), but no similar result was known for non-orientable surfaces.

math.CO↗

arXiv2011

Inside Trading, Public Disclosure and Imperfect Competition

In this paper, we present a multi-period trading model in the style of Kyle (1985)'s inside trading model, by assuming that there are at least two insiders in the market with long-lived private information, under the requirement that each insider publicly discloses his stock trades after the fact. Based on this model, we study the influences of "public disclosure" and "competition among insiders" on the trading behaviors of insiders. We find that the "competition among insiders" leads to higher effective price and lower insiders' profits, and the "public disclosure" makes each insider play a mixed strategy in every round except the last one. An interesting find is that as the total number of auctions goes to infinity, the market depth and the trading intensity at the first auction are all constants with the requirement of "public disclosure", while the market depth at the first auction goes to zero and the trading intensity of the first period goes to infinity without the requirement of "public disclosure".Moreover, we give the exact speed of the revelation of the private information, and show that all information is revealed immediately and the market depth goes to infinity immediately as trading happens infinitely frequently.

q-fin.TR↗

arXiv2011

Holographic non-Fermi liquid fixed points

Techniques arising from string theory can be used to study assemblies of strongly-interacting fermions. Via this `holographic duality', various strongly-coupled many body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared fixed point theory which is represented by an AdS_2 region in the dual gravitational description. Here we describe in detail the gravity calculation of this IR correlation function. This article is a contribution to a special issue of Phil. Trans. A on the normal state of the cuprates; as such, we also provide some review and context.

hep-th↗

arXiv2010

Jet Quenching Parameter via Soft Collinear Effective Theory (SCET)

We analyze the transverse momentum broadening in the absence of radiation of an energetic parton propagating through quark-gluon plasma via Soft Collinear Effective Theory (SCET). We show that the probability for picking up transverse momentum k_\perp is given by the Fourier transform of the expectation value of two transversely separated light-like path-ordered Wilson lines. The subtleties about the ordering of operators do not change the \hat q value for the strongly coupled plasma of N=4 SYM theory.

hep-ph↗

arXiv2010

Radiation of a circulating quark in strongly coupled N=4 super Yang-Mills theory

The energy density and angular distribution of power radiated by a quark undergoing circular motion in strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory is computed using gauge/gravity duality. The results are qualitatively similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: At large velocities the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle $α\sim 1/γ$ and radial thickness scaling like $\sim 1/γ^3$.

hep-th↗

arXiv2010

From black holes to strange metals

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

hep-th↗

arXiv2010

A controlled expansion for certain non-Fermi liquid metals

The destruction of Fermi liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a new controlled theoretical approach to determining the low energy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter ε= z_b -2 where z_b is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low energy physics of these problems. The method is illustrated by studying spinon fermi surface spin liquids, and a quantum critical metal at a second order electronic nematic phase transition. We calculate the low energy single particle spectra, and various interesting two particle correlation functions. In some cases deviations from the popular Random Phase Approximation results are found. Some of the same universal singularities are also calculated to leading non-vanishing order using a perturbative renormalization group calculation at small N extending previous results of Nayak and Wilczek. Implications for quantum spin liquids, and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition we show that the tunneling density of states has a power law suppression at low energies.

cond-mat.str-el↗

arXiv2010

Quantum phase transitions in holographic models of magnetism and superconductors

We study a holographic model realizing an "antiferromagnetic" phase in which a global SU(2) symmetry representing spin is broken down to a U(1) by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged AdS black hole. We observe that the phase transition for both neutral and charged (as in the standard holographic superconductor) order parameters can be driven to zero temperature by a tuning of the UV conformal dimension of the order parameter, resulting in a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type. We also characterize the antiferromagnetic phase and an externally forced ferromagnetic phase by showing that they contain the expected spin waves with linear and quadratic dispersions respectively.

hep-th↗

arXiv2009

Real-time response in AdS/CFT with application to spinors

We discuss a simple derivation of the real-time AdS/CFT prescription as an analytic continuation of the corresponding problem in Euclidean signature. We then extend the formalism to spinor operators and apply it to the examples of real-time fermionic correlators in CFTs dual to pure AdS and the BTZ black hole.

hep-th↗

arXiv2009

Non-Fermi liquids from holography

We report on a potentially new class of non-Fermi liquids in (2+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.

hep-th↗

arXiv2008

Condensed matter physics of a strongly coupled gauge theory with quarks: some novel features of the phase diagram

We revisit the phase diagram of the N=4 SU(N_c) super-Yang-Mills theory coupled to N_f fundamental "quarks" at strong coupling using the gauge-gravity correspondence. We show that in the plane of temperature v.s. baryon chemical potential there is a critical line of third order phase transition which ends at a tricritical point after which the transition becomes first order. Close to the critical line there is an intriguing logarithmic behavior, which cannot follow from a mean field type of analysis. We argue that on the string theory side the third order phase transition is driven by the condensation of worldsheet instantons and that this transition might become a smooth crossover at finite 't Hooft coupling.

hep-th↗

arXiv2008

Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm

We show that at the level of linear response the low frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e. by the "membrane paradigm" fluid of classical black hole mechanics. Thus generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.

hep-th↗

arXiv2008

A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes

We derive a quantization formula of Bohr-Sommerfeld type for computing quasinormal frequencies for scalar perturbations in an AdS black hole in the limit of large scalar mass or spatial momentum. We then apply the formula to find poles in retarded Green functions of boundary CFTs on $R^{1,d-1}$ and $RxS^{d-1}$. We find that when the boundary theory is perturbed by an operator of dimension $Δ>> 1$, the relaxation time back to equilibrium is given at zero momentum by ${1 \over ΔπT} << {1 \over πT}$. Turning on a large spatial momentum can significantly increase it. For a generic scalar operator in a CFT on $R^{1,d-1}$, there exists a sequence of poles near the lightcone whose imaginary part scales with momentum as $p^{-{d-2 \over d+2}}$ in the large momentum limit. For a CFT on a sphere $S^{d-1}$ we show that the theory possesses a large number of long-lived quasiparticles whose imaginary part is exponentially small in momentum.

gr-qc↗

arXiv2008

Stirring Strongly Coupled Plasma

We determine the energy it takes to move a test quark along a circle of radius L with angular frequency w through the strongly coupled plasma of N=4 supersymmetric Yang-Mills (SYM) theory. We find that for most values of L and w the energy deposited by stirring the plasma in this way is governed either by the drag force acting on a test quark moving through the plasma in a straight line with speed v=Lw or by the energy radiated by a quark in circular motion in the absence of any plasma, whichever is larger. There is a continuous crossover from the drag-dominated regime to the radiation-dominated regime. In the crossover regime we find evidence for significant destructive interference between energy loss due to drag and that due to radiation as if in vacuum. The rotating quark thus serves as a model system in which the relative strength of, and interplay between, two different mechanisms of parton energy loss is accessible via a controlled classical gravity calculation. We close by speculating on the implications of our results for a quark that is moving through the plasma in a straight line while decelerating, although in this case the classical calculation breaks down at the same value of the deceleration at which the radiation-dominated regime sets in.

hep-ph↗

arXiv2008

Robustness and Infrared Sensitivity of Various Observables in the Application of AdS/CFT to Heavy Ion Collisions

We investigate the robustness with respect to nonconformality of five properties of strongly coupled plasmas that have been calculated in N=4 supersymmetric Yang-Mills (SYM) theory at nonzero temperature, motivated by the goal of understanding phenomena in heavy ion collisions. (The properties are the jet quenching parameter, the velocity dependence of screening, and the drag and transverse and longitudinal momentum diffusion coefficients for a heavy quark pulled through the plasma.) We use a toy model in which nonconformality is introduced via a one-parameter deformation of the AdS black hole dual to the hot N=4 SYM plasma. Upon introducing a degree of nonconformality comparable to that seen in lattice calculations of QCD at temperatures a few times that of the crossover to quark-gluon plasma, we find that the jet quenching parameter is affected by the nonconformality by at most 30%, the screening length is affected by at most 20%, but the drag and diffusion coefficients for a slowly moving heavy quark can be modified by as much as 80%. However, four of the five properties that we investigate become completely insensitive to the nonconformality in the limit v -> 1. The exception is the jet quenching parameter, which is "infrared sensitive" even at v=1, where it is defined. It is the only high-velocity observable that we investigate which is sensitive to properties of the medium at infrared energy scales proportional to T, namely the scales where the quark-gluon plasma of QCD can be strongly coupled. The other four quantities all probe only scales that are larger than T by a factor that diverges as v -> 1, namely scales where the N=4 SYM plasma can be strongly coupled but the quark-gluon plasma of QCD is not.

hep-ph↗