arXiv subjects

Chaolun Wu

Publications and source records attributed to Chaolun Wu.

13 recordsLinked to original sources

arXiv2016

A Holographic Model for Pseudogap in BCS-BEC Crossover (I): Pairing Fluctuations, Double-Trace Deformation and Dynamics of Bulk Bosonic Fluid

We build a holographic model for the pairing fluctuation pseudogap phase in fermionic high temperature superconductivity/superfluidity based on the BCS-BEC crossover scenario. The pseudogap originates from incoherent Cooper pairing and has been observed in recent cold atom experiments. The strength of Cooper pairing and hence the BCS-BEC crossover is controlled by an effective 4-Fermi interaction and we argue that the double-trace deformation for charged scalar operator is a close analog in large N field theories. We employ the double-trace deformed Abelian Higgs model of holographic superconductors and propose that the incoherent fluctuations of the charged scalar in the bulk is the holographic dual of the fluctuating Cooper pairs. Using a Madelung transformation and the velocity-potential formalism, we develop a quantum fluid dynamics as an effective theory for these bulk fluctuations. The new fluid dynamics takes care of the boundary conditions required by AdS/CFT and encodes the vacuum polarization effect in curved spacetime. The pseudogap in conductivity can be related to the plasma oscillation of this bulk fluid.

hep-th↗

arXiv2015

Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories

We show that the relativistic gravity theory can offer a framework to formulate the non-relativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2+1 dimensions which is particularly appropriate for the study on quantum Hall effects and chiral superfluids. We discuss how the non-relativistic spacetime structure emerges from relativistic gravity. We present covariant maps and constraints that relate the field contents in the two theories, which also serve as the holographic dictionary in context of gauge/gravity duality. A low energy effective action for fractional quantum Hall states is constructed, which captures universal geometric properties and generates non-universal corrections systematically. We give another holographic example with dyonic black brane background to calculate thermodynamic and transport properties of strongly coupled non-relativistic fluids in magnetic field. In particular, by identifying the shift function in the gravity as minus of guiding center velocity, we obtain the Hall viscosity with its relation to Landau orbital angular momentum density proportional to Wen-Zee shift. Our formalism has a good projection to lowest Landau level.

hep-th↗

arXiv2014

Angular Momentum Generation from Holographic Chern-Simons Models

We study parity-violating effects, particularly the generation of angular momentum density and its relation to the parity-odd and dissipationless transport coefficient Hall viscosity, in strongly-coupled quantum fluid systems in 2+1 dimensions using holographic method. We employ a class of 3+1-dimensional holographic models of Einstein-Maxwell system with gauge and gravitational Chern-Simons terms coupled to a dynamical scalar field. The scalar can condensate and break the parity spontaneously. We find that when the scalar condensates, a non-vanishing angular momentum density and an associated edge current are generated, and they receive contributions from both gauge and gravitational Chern-Simons terms. The angular momentum density does not satisfy a membrane paradigm form because the vector mode fluctuations from which it is calculated are effectively massive. On the other hand, the emergence of Hall viscosity is a consequence of the gravitational Chern-Simons term alone and it has membrane paradigm form. We present both general analytic results and numeric results which take back-reactions into account. The ratio between Hall viscosity and angular momentum density resulting from the gravitational Chern-Simons term has in general a deviation from the universal 1/2 value obtained from field theory and condensed matter physics.

hep-th↗

arXiv2014

Lowest Landau Level Stress Tensor and Structure Factor of Trial Quantum Hall Wave Functions

We show that for a class of model Hamiltonians for which certain trial quantum Hall wavefunctions are exact ground states, there is a single spectral density function which controls all two-point correlation functions of density, current and stress tensor components. From this we show that the static structure factors of these wavefunctions behaves at long wavelengths as $s_4 k^4$ where the coefficient $s_4$ is directly related to the shift: $s_4=(\mathcal S-1)/8$.

cond-mat.str-el↗

arXiv2014

Spacetime Symmetries of the Quantum Hall Effect

We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism invariance studied in previous work is enhanced to a full spacetime symmetry, allowing us to derive a number of Ward identities. These symmetries are smooth in the massless limit of the lowest Landau level. We develop a formalism for Newton-Cartan geometry with torsion to write these Ward identities in a covariant form. Previous results on the connection between Hall viscosity and Hall conductivity are reproduced.

cond-mat.mes-hall↗

arXiv2014

Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect

We show that Horava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Horava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Horava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.

hep-th↗

arXiv2014

Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum

We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe strongly-coupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant but allows a black hole solution with vector hair corresponding to a parity-broken superfluid state. We show that this state possesses a non-vanishing parity-odd transport coefficient -- Hall viscosity -- and an angular momentum density. We first develop an analytic method to solve this model near the critical regime and to take back-reactions into account. Then we solve the equation for the tensor mode fluctuations and obtain the expression for Hall viscosity via Kubo formula. We also show that a non-vanishing angular momentum density can be obtained through the vector mode fluctuations and the corresponding boundary action. We give analytic results of both Hall viscosity and angular momentum density near the critical regime in terms of physical parameters. The near-critical behavior of Hall viscosity is different from that obtained from a gravitational Chern-Simons model. We find that the magnitude of Hall viscosity to angular momentum density ratio is numerically consistent with being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in agreement with previous results obtained for various quantum fluid systems and from effective theory approaches. In addition, we find the shear viscosity to entropy density ratio remains above the universal bound.

hep-th↗

arXiv2012

On the 3-point functions of Aging Dynamics and the AdS/CFT Correspondence

Aging can be realized as a sub-algebra of Schrödinger algebra by discarding the time-translation generator. While the 2-point functions of the Age algebra have been known for some time, little else was known about the higher $n$-point correlators. In this letter we present novel 3-point correlators of scalar primary operators. We find that the Aging correlators are distinct from the Schrödinger correlators by more than certain dressings with time-dependent factors, as was the case with 2-point functions. In the existing literature, the holographic geometry of Aging is obtained by performing certain general coordinate transformations on the holographic dual of the Schrödinger theory. Consequently, the Aging 2-point functions derived from holography look as the Schrödinger 2-point functions dressed by time-dependent factors. However, since the 3-point functions obtained in this letter are not merely dressed Schrödinger correlators and instead depend on an additional time-translation breaking variable, we conclude that the most general holographic realization of Aging is yet to be found.

hep-th↗

arXiv2011

Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT

We study second order relativistic viscous hydrodynamics in 4-dimensional conformal field theories. We derive Kubo-type relations for second order hydrodynamic coefficients in terms of 3-point stress tensor retarded correlators. For N=4 super Yang-Mills theory at strong coupling and at finite temperature we compute these stress tensor 3-point correlators, using AdS/CFT, by evaluating real-time cubic Witten diagrams in the AdS-Schwarzschild background. The small momentum expansion of the 3-point correlators in terms of first and second order hydrodynamic coefficients is matched with the AdS result. We arrive at the same expressions for the hydrodynamic coefficients which multiply terms quadratic in the shear and vorticity tensors in the hydrodynamic expansion of the stress tensor as did Bhattacharyya, Hubeny, Minwalla and Rangamani \cite{Bhattacharyya:2008jc}. Our method extends the results of Baier et al \cite{Baier:2007ix}, and allows for a unified treatment of hydrodynamic coefficients, which are extracted from 2-, and now, 3-point retarded stress tensor correlators in the AdS-Schwarzschild background.

hep-th↗

arXiv2010

Holographic real-time non-relativistic correlators at zero and finite temperature

We compute a variety of two and three-point real-time correlation functions for a strongly-coupled non-relativistic field theory. We focus on the theory conjectured to be dual to the Schrödinger-invariant gravitational spacetime introduced by Balasubramanian, McGreevy, and Son, but our methods apply to a large class of non-relativistic theories. At zero temperature, we obtain time-ordered, retarded, and Wightman non-relativistic correlators for scalar operators of arbitrary conformal dimension directly in field theory by applying a certain lightlike Fourier transform to relativistic conformal correlators, and we verify that non-relativistic AdS/CFT reproduces the results. We compute thermal two and three-point real-time correlators for scalar operators dual to scalar fields in the black hole background which is the finite temperature generalization of the Schrödinger spacetime. This is done by first identifying thermal real-time bulk-to-boundary propagators, which combined with Veltman's circling rules, yield two and three-point correlators. The two-point correlators we obtain satisfy the Kallen-Lehmann relations. We also give retarded and time-ordered three-point correlators.

hep-th↗

arXiv2010

Real-time finite-temperature correlators from AdS/CFT

In this paper we use AdS/CFT ideas in conjunction with insights from finite temperature real-time field theory formalism to compute 3-point correlators of ${\cal N}{=}4$ super Yang-Mills operators, in real time and at finite temperature. To this end, we propose that the gravity field action is integrated only over the right and left quadrants of the Penrose diagram of the Anti de Sitter-Schwarzschild background, with a relative sign between the two terms. For concreteness we consider the case of a scalar field in the black hole background. Using the scalar field Schwinger-Keldysh bulk-to-boundary propagators, we give the general expression of a 3-point real-time Green's correlator. We then note that this particular prescription amounts to adapting the finite-temperature analog of Veltman's circling rules to tree-level Witten diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary propagators. We subject our prescription to several checks: KMS identities, the largest time equation and the zero-temperature limit. When specializing to a particular retarded (causal) 3-point function, we find a very simple answer: the momentum-space correlator is given by three causal (two retarded and one advanced) bulk-to-boundary propagators, meeting at a vertex point which is integrated from spatial infinity to the horizon only. This result is expected based on analyticity, since the retarded n-point functions are obtained by analytic continuation from the imaginary time Green's function, and based on causality considerations.

hep-th↗

arXiv2009

All 4-dimensional static, spherically symmetric, 2-charge abelian Kaluza-Klein black holes and their CFT duals

We derive the dual CFT Virasoro algebras from the algebra of conserved diffeomorphism charges, for a large class of abelian Kaluza-Klein black holes. Under certain conditions, such as non-vanishing electric and magnetic monopole charges, the Kaluza-Klein black holes have a Reissner-Nordstrom space-time structure. For the non-extremal charged Kaluza-Klein black holes, we use the uplifted 6d pure gravity solutions to construct a set of Killing horizon preserving diffeomorphisms. For the (non-supersymmetric) extremal black holes, we take the NENH limit, and construct a one-parameter family of diffeomorphisms which preserve the Hamiltonian constraints at spatial infinity. In each case we evaluate the algebra of conserved diffeomorphism charges following Barnich, Brandt and Compere, who used a cohomological approach, and Silva, who employed a covariant-Lagrangian formalism. At the Killing horizon, it is only Silva's algebra which acquires a central charge extension, and which enables us to recover the Bekenstein-Hawking black hole entropy from the Cardy formula. For the NENH geometry, the extremal black hole entropy is obtained only when the free parameter of the diffeomorphism generating vector fields is chosen such that the central terms of the two algebras are in agreement.

hep-th↗

arXiv2007

The mass and luminosity functions and the formation rate of DA white dwarfs in the Sloan Digital Sky Survey

The SDSS Data Release 1 includes 1833 DA white dwarfs (WDs) and forms the largest homogeneous sample of WDs. This sample provides the best opportunity to study the statistical properties of WDs. We adopt a recently established theoretical model to calculate the mass and distance of each WD using the observational data. Then we adopt a bin-correction method to correct for selection effects and use the 1/V weight-factor method to calculate the luminosity function, the continuous mass function and the formation rate of these WDs. The SDSS DA WD sample is incomplete and suffers seriously from selection effects. After corrections for the selection effects, only 531 WDs remain. From this final sample we derive the most up-to-date luminosity function and mass function, in which we find a broad peak of WD masses centered around 0.58$M_{\odot}$. The DA WD space density is calculated as $8.81\times10^{-5}pc^{-3}$ and the formation rate is $2.579\times 10^{-13}pc^{-3}yr^{-1}$. The statistical properties of the SDSS DA WD sample are generally in good agreement with previous observational and theoretical studies, and provide us information on the formation and evolution of WDs. However, a larger and more complete all-sky WD sample is still needed to explain some subtle disagreements and unresolved issues.

astro-ph↗