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Results for “Renormalization Group”
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Gluon polarization in the proton
We combine heavy-quark renormalization group arguments with our understanding of the nucleon's wave function to deduce a bound on the gluon polarization {Delta}g in the proton. The bound is consistent with the values extracted from spin experiments at COMPASS and RHIC.
Phase transitions in dipolar spin-1 Bose gases
We study phase transitions in homogeneous spin-1 Bose gases in the presence of long-range magnetic dipole-dipole interactions (DDI). We concentrate on three-dimensional (3D) geometries and employ momentum shell renormalization group to study the possible instabilities caused by the DDI. At the zero-temperature limit where quantum fluctuations prevail, we find the phase diagram to be unaffected by the DDI. When the thermal fluctuations dominate, polar and ferromagnetic condensates with DDI become unstable and we discuss this crossover in detail. On the other hand, the spin-singlet condensate remains stable in the presence of DDI.
Generational structure of models with dynamical symmetry breaking
In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably ultraviolet-complete theories of this type, the number of stages of breaking of the larger gauge symmetry is usually equal to the observed number of quark and lepton generations, N{sub gen}=3. Here we investigate the general question of how the construction and properties of these models depend on N{sub gen}, regarded as a variable. We build and analyze models with illustrative values of N{sub gen} different from 3 (namely N{sub gen}=1,2,4) that exhibit the necessary sequential symmetry breaking down to a strongly coupled sector that dynamically breaks electroweak symmetry. Our results for variable N{sub gen} show that one can robustly obtain, for this latter sector, a theory with a gauge coupling that is large but slowly running, controlled by an approximate infrared fixed point of the renormalization group. Owing to this, we find that for all of the values of N{sub gen} considered, standard-model fermions of the highest generation have masses that can be comparable to the electroweak-symmetry-breaking scale. We also study the interplay of multiple strongly coupled gauge symmetries in these models.
Relaxation dynamics in correlated quantum dots
We study quantum many-body effects on the real-time evolution of the current through quantum dots. By using a non-equilibrium renormalization group approach, we provide analytic results for the relaxation dynamics into the stationary state and identify the microscopic cutoff scales that determine the transport rates. We find rich non-equilibrium physics induced by the interplay of the different energy scales. While the short-time limit is governed by universal dynamics, the long-time behavior features characteristic oscillations as well as an interplay of exponential and power-law decay.
Recent progress in backreacted bottom-up holographic QCD
Recent progress in constructing holographic models for QCD is discussed, concentrating on the bottom-up models which implement holographically the renormalization group flow of QCD. The dynamics of gluons can be modeled by using a string-inspired model termed improved holographic QCD, and flavor can be added by introducing space filling branes in this model. The flavor fully backreacts to the glue in the Veneziano limit, giving rise to a class of models which are called V-QCD. The phase diagrams and spectra of V-QCD are in good agreement with results for QCD obtained by other methods.
Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions
Research highlights: {yields}Dephasing rate due to short-range e-e interaction at Anderson transitions is analyzed. {yields}The operators controlling the scaling of the dephasing rate are idenitified. {yields}Dephasing rate exponent is estimated for the quantum Hall transition. - Abstract: We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + {epsilon} dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.
Operator product expansion algebra
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE, =Σ{sub C}C{sub A{sub 1A{sub 2A{sub 3}{sup C}}}} , usually interpreted only as an asymptotic short distance expansion, actually converges at finite, and even large, distances. We further show that the factorization identity C{sub A{sub 1A{sub 2A{sub 3}{sup B}}}}=Σ{sub C}C{sub A{sub 1A{sub 2}{sup C}}}C{sub CA{sub 3}{sup B}} is satisfied for suitable configurations of the spacetime arguments. Again, the infinite sum is shown to be convergent. Our proofs rely on explicit bounds on the remainders of these expansions, obtained using refined versions, mostly due to Kopper et al., of the renormalization group flow equation method. These bounds also establish that each OPE coefficient is a real analytic function in the spacetime arguments for non-coinciding points. Our results hold for arbitrary but finite loop orders. They lend support to proposals for a general axiomatic framework of quantum field theory, based on such “consistency conditions” and akin to vertex operator algebras, wherein the OPE is promoted to the defining structure of the theory.
Soft spectator scattering in the nucleon form factors at large Q{sup 2} within the soft collinear effective theory approach
The proton form factors at large momentum transfer are dominated by two contributions which are associated with the hard and soft rescattering, respectively. Motivated by a very active experimental form factor program at intermediate values of momentum transfers, Q{sup 2}{approx}5-15 GeV{sup 2}, where an understanding in terms of only a hard rescattering mechanism cannot yet be expected, we investigate in this work the soft rescattering contribution using soft collinear effective theory (SCET). Within such a description, the form factor is characterized, besides the hard scale Q{sup 2}, by a hard-collinear scale Q{Lambda}, which arises due to the presence of soft spectators, with virtuality {Lambda}{sup 2} ({Lambda}{approx}0.5 GeV), such that Q{sup 2}>>Q{Lambda}>>{Lambda}{sup 2}. We show that in this case a two-step factorization can be successfully carried out using the SCET approach. In a first step (SCET{sub I}), we perform the leading-order matching of the QCD electromagnetic current onto the relevant SCET{sub I} operators and perform a resummation of large logarithms using renormalization group equations. We then discuss the further matching onto a SCET{sub II} framework, and propose the factorization formula (accurate to leading logarithmic approximation) for the Dirac form factor, accounting for both hard and soft contributions. We also present a qualitative discussion of the phenomenological consequences of this new framework.
Interacting preformed Cooper pairs in resonant Fermi gases
We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozieres-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi et al. [Science 327, 442 (2010)] and Nascimbene et al. [Nature (London) 463, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, which can be tested in experiments.
Asymptotic safety and Kaluza-Klein gravitons at the LHC
We study Drell-Yan production at the LHC in low-scale quantum gravity models with extra dimensions. Asymptotic safety implies that the ultraviolet behavior of gravity is dictated by a fixed point. We show how the energy dependence of Newton's coupling regularizes the gravitational amplitude using a renormalization group improvement. We study LHC predictions and find that Kaluza-Klein graviton signals are well above standard model backgrounds. This leaves a significant sensitivity to the energy scale {Lambda}{sub T} where the gravitational couplings crossover from classical to fixed point scaling.
{eta} Condensate of Fermionic Atom Pairs via Adiabatic State Preparation
We discuss how an {eta} condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalization group methods, we analyze a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
Crumpled-to-Tubule Transition in Anisotropic Polymerized Membranes: Beyond the {epsilon} Expansion
Anisotropic D-dimensional polymerized phantom membranes are investigated within a nonperturbative renormalization group framework. One focuses on the transition between a high-temperature, crumpled phase and a low-temperature, tubular phase where the membrane is flat along one direction and crumpled along the other ones. While the upper critical dimension--D{sub uc}=5/2--is close to D=2, the weak-coupling perturbative approach is qualitatively and quantitatively wrong. We show that our approach is free of the problems encountered within the perturbative framework and provides physically meaningful critical quantities.
Berezinskii-Kosterlitz-Thouless transition uncovered by the fidelity susceptibility in the XXZ model
We investigate the one-dimensional Heisenberg XXZ model involving the Dzyaloshinskii-Moriya (DM) interaction from the viewpoint of quantum information. By using the density-matrix-renormalization-group technique, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the ground-state fidelity, the fidelity susceptibility, and the entanglement entropy. We argue that the BKT phase transition can be well characterized in our model, and the critical line induced by the DM interaction can also be detected.
Flat electronic bands in fractal-kagomé network and the effect of perturbation
We demonstrate an analytical prescription of demonstrating the flat band [FB] states in a fractal incorporated kagomé type network that can give rise to a countable infinity of flat non-dispersive eigenstates with a multitude of localization area. The onset of localization can, in principle, be delayed in space by an appropriate choice of energy regime. The length scale, at which the onset of localization for each mode occurs, can be tuned at will following the formalism developed within the framework of real space renormalization group. This scheme leads to an exact determination of energy eigenvalue for which one can have dispersionless flat electronic bands. Furthermore, we have shown the effect ofuniform magnetic field for the same non-translationally invariant network model that has ultimately led to an‘apparent invisibility’ of such staggered localized states and to generate absolutely continuous sub-bands in the energy spectrum and again an interesting re-entrant behavior of those FB states.
A zeroth-order active-space frozen-orbital embedding scheme for multireference calculations
Multireference computations of large-scale chemical systems are typically limited by the computational cost of quantum chemistry methods. In this work, we develop a zeroth-order active space embedding theory [ASET(0)], a simple and automatic approach for embedding any multireference dynamical correlation method based on a frozen-orbital treatment of the environment. ASET(0) is combined with the second-order multireference driven similarity renormalization group and tested on several benchmark problems, including the excitation energy of 1-octene and bond-breaking in ethane and pentyldiazene. Finally, we apply ASET(0) to study the singlet–triplet gap of p-benzyne and 9,10-anthracyne diradicals adsorbed on a NaCl surface. Our results show that despite its simplicity, ASET(0) is a powerful and sufficiently accurate embedding scheme applicable when the coupling between the fragment and the environment is in the weak to medium regime.
Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas
We study a one-dimensional Fermi gas with attractive short range-interactions in a disordered potential by the density matrix renormalization group (DMRG) technique. Our results can be tested experimentally by using cold atom techniques. We identify a region of parameters for which disorder enhances the superfluid state. As disorder is further increased, global superfluidity eventually breaks down. However this transition seems to occur before the transition to the insulator state takes place. This suggests the existence of an intermediate metallic 'pseudogap' phase characterized by strong pairing but no quasi-long-range order.
Non-Fermi-Liquid Fixed Point for an Imbalanced Gas of Fermions in 1+{epsilon} Dimensions
We consider a gas of two species of fermions with population imbalance. Using the renormalization group in d=1+{epsilon} spatial dimensions, we show that for spinless fermions and 2>{epsilon}>0 a fixed point appears at finite attractive coupling where the quasiparticle residue vanishes, and identify this with the transition to Larkin-Ovchinnikov-Fulde-Ferrell order (inhomogeneous superconductivity). When the two species of fermions also carry spin degrees of freedom we find a fixed point indicating a transition to spin density wave order.