arXiv subjects

Hong Liu

Publications and source records attributed to Hong Liu.

At least 487 records · Page 27Linked to original sources

arXiv2013

A refinement of entanglement entropy and the number of degrees of freedom

We introduce a "renormalized entanglement entropy" which is intrinsically UV finite and is most sensitive to the degrees of freedom at the scale of the size R of the entangled region. We illustrated the power of this construction by showing that the qualitative behavior of the entanglement entropy for a non-Fermi liquid can be obtained by simple dimensional analysis. We argue that the functional dependence of the "renormalized entanglement entropy" on R can be interpreted as describing the renormalization group flow of the entanglement entropy with distance scale. The corresponding quantity for a spherical region in the vacuum, has some particularly interesting properties. For a conformal field theory, it reduces to the previously proposed central charge in all dimensions, and for a general quantum field theory, it interpolates between the central charges of the UV and IR fixed points as R is varied from zero to infinity. We conjecture that in three (spacetime) dimensions, it is always non-negative and monotonic, and provides a measure of the number of degrees of freedom of a system at scale R. In four dimensions, however, we find examples in which it is neither monotonic nor non-negative.

hep-th↗

arXiv2013

Multicolor Ramsey numbers for triple systems

Given an $r$-uniform hypergraph $H$, the multicolor Ramsey number $r_k(H)$ is the minimum $n$ such that every $k$-coloring of the edges of the complete $r$-uniform hypergraph $K_n^r$ yields a monochromatic copy of $H$. We investigate $r_k(H)$ when $k$ grows and $H$ is fixed. For nontrivial 3-uniform hypergraphs $H$, the function $r_k(H)$ ranges from $\sqrt{6k}(1+o(1))$ to double exponential in $k$. We observe that $r_k(H)$ is polynomial in $k$ when $H$ is $r$-partite and at least single-exponential in $k$ otherwise. Erdős, Hajnal and Rado gave bounds for large cliques $K_s^r$ with $s\ge s_0(r)$, showing its correct exponential tower growth. We give a proof for cliques of all sizes, $s>r$, using a slight modification of the celebrated stepping-up lemma of Erdős and Hajnal. For 3-uniform hypergraphs, we give an infinite family with sub-double-exponential upper bound and show connections between graph and hypergraph Ramsey numbers. Specifically, we prove that $$r_k(K_3)\le r_{4k}(K_4^3-e)\le r_{4k}(K_3)+1,$$ where $K_4^3-e$ is obtained from $K_4^3$ by deleting an edge. We provide some other bounds, including single-exponential bounds for $F_5=\{abe,abd,cde\}$ as well as asymptotic or exact values of $r_k(H)$ when $H$ is the bow $\{abc,ade\}$, kite $\{abc,abd\}$, tight path $\{abc,bcd,cde\}$ or the windmill $\{abc,bde,cef,bce\}$. We also determine many new "small" Ramsey numbers and show their relations to designs. For example, the lower bound for $r_6(kite)=8$ is demonstrated by decomposing the triples of $[7]$ into six partial STS (two of them are Fano planes).

math.CO↗

arXiv2013

Manipulating the magnetic anisotropy of cobalt doped titanium dioxide by carrier accumulation

Based on first-principles calculations, we predict that the magnetic anisotropy energy (MAE) of Co-doped TiO$_2$ sensitively depends on carrier accumulation. This magnetoelectric phenomenon provides a promising route to directly manipulate the magnetization direction of diluted magnetic semiconductor by external electric-fields. We calculate the band structures and reveal the origin of carrier-dependent MAE in k-space. In fact, the carrier accumulation shifts the Fermi energy and regulates the competing contributions to MAE. The first-principles calculations provide a straightforward way to design spintronics materials with electrically controllable spin direction.

cond-mat.mtrl-sci↗

arXiv2013

Ab initio study of magnetic anisotropy in cobalt doped zinc oxide with electron-filling

Based on first-principles calculation, it has been predicted that the magnetic anisotropy energy (MAE) in Co-doped ZnO (Co:ZnO) depends on electron-filling. Results show that the charge neutral Co:ZnO presents a "easy plane" magnetic state. While modifying the total number of electrons, the easy axis rotates from in-plane to out-of-plane. The alternation of the MAE is considered to be the change of the ground state of Co ion, resulting from the relocating of electrons on Co d-orbitals with electron-filling.

cond-mat.mtrl-sci↗

arXiv2012

Holographic Vortex Liquids and Superfluid Turbulence

Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by mapping the dynamics of certain quantum theories onto the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov -5/3 scaling law, as it does for turbulent flows in normal fluids. We trace this scaling to a direct energy cascade by injecting energy at long wavelengths and watching it flow to a short-distance scale set by the vortex core size, where dissipation by vortex annihilation and vortex drag becomes efficient. This is in sharp contrast with the inverse energy cascade of normal fluid turbulence in two dimensions. We also demonstrate that the microscopic dissipation spectrum has a simple geometric interpretation.

hep-th↗

arXiv2012

On coloring of fractional powers of graphs

For $m, n\in \N$, the fractional power $\Gmn$ of a graph $G$ is the $m$th power of the $n$-subdivision of $G$, where the $n$-subdivision is obtained by replacing each edge in $G$ with a path of length $n$. It was conjectured by Iradmusa that if $G$ is a connected graph with $Δ(G)\ge 3$ and $1 ω(H^{3/5})$. However, we prove that the conjecture is true if $m$ is even. We also study the case when $m$ is odd, obtaining a general upper bound $χ(\Gmn)\leq ω(\Gmn)+2$ for graphs with $Δ(G)\geq 4$.

math.CO↗

arXiv2012

Momentum Broadening in Weakly Coupled Quark-Gluon Plasma (with a view to finding the quasiparticles within liquid quark-gluon plasma)

We calculate P(k_\perp), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k_\perp, for a medium consisting of weakly coupled quark-gluon plasma. We use full or HTL self-energies in appropriate regimes, resumming each in order to find the leading large-L behavior. The jet quenching parameter \hat q is the second moment of P(k_\perp), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P(k_\perp) in its entirety. We compare our results for P(k_\perp) in weakly coupled quark-gluon plasma to expectations from holographic calculations that assume a plasma that is strongly coupled at all length scales. We find that the shape of P(k_\perp) at modest k_\perp may not be very different in weakly coupled and strongly coupled plasmas, but we find that P(k_\perp) must be parametrically larger in a weakly coupled plasma than in a strongly coupled plasma at large enough k_\perp. This means that by looking for rare (but not exponentially rare) large-angle deflections of the jet resulting from a parton produced initially back-to-back with a hard photon, experimentalists can find the weakly coupled short-distance quark and gluon quasiparticles within the strongly coupled liquid quark-gluon plasma produced in heavy ion collisions, much as Rutherford found nuclei within atoms or Friedman, Kendall and Taylor found quarks within nucleons.

hep-ph↗

arXiv2012

Ab initio calculation of the local magnetic moment in titanium doped zinc oxide with a corrected-band-gap scheme

The local magnetic moment of Ti:ZnO is calculated from first principles by using the corrected-band-gap scheme (CBGS). The results shows that the system is magnetic with the magnetization of 0.699 $μ_B$ per dopant. The origin of the local magnetic moment is considered to be the impurity band partially occupied by the donor electrons in the conduction band. Further, the impacts of applying Hubbard U to Ti-d orbital on the magnetic moment have been investigated.

cond-mat.mtrl-sci↗

arXiv2012

Extremal graphs for blow-ups of cycles and trees

The \emph{blow-up} of a graph $H$ is the graph obtained from replacing each edge in $H$ by a clique of the same size where the new vertices of the cliques are all different. Erdős et al. and Chen et al. determined the extremal number of blow-ups of stars. Glebov determined the extremal number and found all extremal graphs for blow-ups of paths. We determined the extremal number and found the extremal graphs for the blow-ups of cycles and a large class of trees, when $n$ is sufficiently large. This generalizes their results. The additional aim of our note is to draw attention to a powerful tool, a classical decomposition theorem of Simonovits.

math.CO↗

arXiv2012

Gauge/String Duality, Hot QCD and Heavy Ion Collisions

Over the last decade, both experimental and theoretical advances have brought the need for strong coupling techniques in the analysis of deconfined QCD matter and heavy ion collisions to the forefront. As a consequence, a fruitful interplay has developed between analyses of strongly-coupled non-abelian plasmas via the gauge/string duality (also referred to as the AdS/CFT correspondence) and the phenomenology of heavy ion collisions. We review some of the main insights gained from this interplay to date. To establish a common language, we start with an introduction to heavy ion phenomenology and finite-temperature QCD, and a corresponding introduction to important concepts and techniques in the gauge/string duality. These introductory sections are written for nonspecialists, with the goal of bringing readers ranging from beginning graduate students to experienced practitioners of either QCD or gauge/string duality to the point that they understand enough about both fields that they can then appreciate their interplay in all appropriate contexts. We then review the current state-of-the art in the application of the duality to the description of the dynamics of strongly coupled plasmas, with emphases that include: its thermodynamic, hydrodynamic and transport properties; the way it both modifies the dynamics of, and is perturbed by, high-energy or heavy quarks passing through it; and the physics of quarkonium mesons within it. We seek throughout to stress the lessons that can be extracted from these computations for heavy ion physics as well as to discuss future directions and open problems for the field.

hep-th↗

arXiv2012

Luttinger's theorem, superfluid vortices, and holography

Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. "fractionalized") charge degrees of freedom.

hep-th↗

arXiv2012

Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube

In this paper we modify slightly Razborov's flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4-cycle-free subgraph of the n-dimensional hypercube is at most 0.6068 times the number of its edges. We also improve the upper bound on the number of edges for 6-cycle-free subgraphs of the n-dimensional hypercube from the square root of 2 - 1 to 0.3755 times the number of its edges. Additionally, we show that if the n-dimensional hypercube is considered as a poset, then the maximum vertex density of three middle layers in an induced subgraph without 4-cycles is at most 2.15121 times n choose n/2.

math.CO↗

arXiv2012

On the Turan number of forests

The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [ Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turan number and extremal graphs for forests consisting of stars of arbitrary order.

math.CO↗

arXiv2011

Emergent quantum criticality, Fermi surfaces, and AdS2

Gravity solutions dual to d-dimensional field theories at finite charge density have a near-horizon region which is AdS_2 x R^{d-1}. The scale invariance of the AdS_2 region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a (0+1)-dimensional CFT. This interpretation sheds light on recently-discovered holographic descriptions of Fermi surfaces, allowing an analytic understanding of their low-energy excitations. For example, the scaling behavior near the Fermi surfaces is determined by conformal dimensions in the emergent IR CFT. In particular, when the operator is marginal in the IR CFT, the corresponding spectral function is precisely of the "Marginal Fermi Liquid" form, postulated to describe the optimally doped cuprates.

hep-th↗

arXiv2011

Momentum Broadening in Weakly Coupled Quark-Gluon Plasma

We calculate the probability distribution P(k_\perp) for the momentum perpendicular to its original direction of motion that an energetic quark or gluon picks up as it propagates through weakly coupled quark-gluon plasma in thermal equilibrium.

hep-ph↗

arXiv2011

Lectures on holographic non-Fermi liquids and quantum phase transitions

In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system arising from the duality, obtained by turning on a nonzero chemical potential for a U(1) global symmetry of a CFT, and described on the gravity side by a charged black hole. We address the following questions of such a finite density system: 1. Does the system have a Fermi surface? What are the properties of low energy excitations near the Fermi surface? 2. Does the system have an instability to condensation of scalar operators? What is the critical behavior near the corresponding quantum critical point? We find interesting parallels with those of high T_c cuprates and heavy electron systems. Playing a crucial role in our discussion is a universal intermediate-energy phase, called a "semi-local quantum liquid", which underlies the non-Fermi liquid and novel quantum critical behavior of a system. It also provides a novel mechanism for the emergence of lower energy states such as a Fermi liquid or a superconductor.

hep-th↗

arXiv2011

Synchrotron radiation in strongly coupled conformal field theories

Using gauge/gravity duality, we compute the energy density and angular distribution of the power radiated by a quark undergoing circular motion in strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory. We compare the strong coupling results to those at weak coupling, and find the same angular distribution of radiated power, up to an overall prefactor. In both regimes, the angular distribution is in fact similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle $α\sim 1/γ$. To an observer far away from the quark, the emitted radiation appears as a short periodic burst, just like the light from a lighthouse does to a ship at sea. Our strong coupling results are valid for any strongly coupled conformal field theory with a dual classical gravity description.

hep-th↗

arXiv2011

Transverse Momentum Broadening and the Jet Quenching Parameter, Redux

We use Soft Collinear Effective Theory (SCET) to analyze the transverse momentum broadening, or diffusion in transverse momentum space, of an energetic parton propagating through quark-gluon plasma. Since we neglect the radiation of gluons from the energetic parton, we can only discuss momentum broadening, not parton energy loss. The interaction responsible for momentum broadening in the absence of radiation is that between the energetic (collinear) parton and the Glauber modes of the gluon fields in the medium. We derive the effective Lagrangian for this interaction, and 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. This yields a field theoretical definition of the jet quenching parameter \hat q, and shows that this can be interpreted as a diffusion constant. We close by revisiting the calculation of \hat q for the strongly coupled plasma of N=4 SYM theory, showing that previous calculations need some modifications that make them more straightforward and do not change the result.

hep-ph↗