Renormalization group for the φ

We calculate the critical exponent η of the D-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the smallness of the inverse range of the interaction and on the assumption that the Ginzburg momentum defining the width of the scaling regime in momentum space is larger than the scale where the renormalized interaction crosses over from long range to short range; the numerical value of η can then be estimated by stopping the renormalization group flow at this scale. In three dimensions our result η=0.03651 is in good agreement with recent conformal bootstrap and Monte Carlo calculations. We extend our calculations to fractional dimensions D and obtain the resulting critical exponent η(D) between two and four dimensions. For dimensions 2≤D≤3 our result for η is consistent with previous calculations.

Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: Irrelevance of amplitude and out-of-plane fluctuations.

We develop a functional renormalization group (FRG) approach for the two-dimensional XY model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)PLEEE81539-375510.1103/PhysRevE.82.041128] with a duality transformation that explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include weak amplitude as well as out-of-plane fluctuations of the spins, which lead to additional interactions between the vortices that do not spoil the Berezinskii-Kosterlitz-Thouless transition. This demonstrates that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.

Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets.

We show that the formation of a magnon condensate in thin ferromagnetic films can be explained within the framework of a classical stochastic non-Markovian Landau-Lifshitz-Gilbert equation where the properties of the random magnetic field and the dissipation are determined by the underlying phonon dynamics. We have numerically solved this equation for a tangentially magnetized yttrium-iron garnet film in the presence of a parallel parametric pumping field. We obtain a complete description of all stages of the nonequilibrium time evolution of the magnon gas which is in excellent agreement with experiments. Our calculation proves that the experimentally observed condensation of magnons in yttrium-iron garnet at room temperature is a purely classical phenomenon which should be called Rayleigh-Jeans rather than Bose-Einstein condensation.

Spectral function and quasiparticle damping of interacting Bosons in two dimensions.

We employ the functional renormalization group to study dynamical properties of the two-dimensional Bose gas. Our approach is free of infrared divergences, which plague the usual diagrammatic approaches, and is consistent with the exact Nepomnyashchy identity, which states that the anomalous self-energy vanishes at zero frequency and momentum. We recover the correct infrared behavior of the propagators and present explicit results for the spectral line shape, from which we extract the quasiparticle dispersion and damping.

Magnetic properties of a novel quasi-2D Cu(II)-trimer system.

We present structural and magnetic data of a new Cu(2+)(S = 1/2)-containing magnetic trimer system 2b·3CuCl(2)·2H(2)O (b = betaine, C(5)H(11)NO(2)). The trimers form a quasi-2D quantum spin system with an unusual intra-layer exchange coupling topology, which, in principle, supports diagonal four-spin exchange. To describe the magnetic properties, a 2D effective interacting-trimer model has been developed including an intra-trimer coupling J and two inter-trimer couplings J(a) and J(b). The low-energy description and effective parameters are obtained from numerical calculations based on four coupled trimers (with periodic boundary conditions). Fits to the experimental data using this model yield the magnetic coupling constants J/k(B) = -15 K and J(a)/k(B) = J(b)/k(B) = -4 K. These parameters describe the susceptibility and magnetization data very well over the whole temperature and field range investigated. Moreover, the model calculations indicate that, for certain ranges of the ratio J(b)/J(a), which might be accessible by either chemical substitution and/or hydrostatic pressure, the low-energy properties of 2b·3CuCl(2)·2H(2)O will be dominated by non-trivial four-spin exchange processes.

A functional renormalization group approach to the Anderson impurity model.

We develop a functional renormalization group approach which describes the low-energy single-particle properties of the Anderson impurity model up to intermediate on-site interactions [Formula: see text], where Δ is the hybridization in the wide-band limit. Our method is based on a generalization of a method proposed by Schütz et al (2005 Phys. Rev. B 72 035107), using two independent Hubbard-Stratonovich fields associated with transverse and longitudinal spin fluctuations. Although we do not reproduce the exponentially small Kondo scale in the limit [Formula: see text], the spin fluctuations included in our approach remove the unphysical Stoner instability predicted by mean field theory for U>πΔ. We discuss different decoupling schemes and show that a decoupling which manifestly respects the spin-rotational invariance of the problem gives rise to the lowest quasiparticle weight. To obtain a closed flow equation for the fermionic self-energy we also propose a new scheme of truncation of the functional renormalization group flow equations using Dyson-Schwinger equations to express bosonic vertex functions in terms of fermionic ones.

Condensate density of interacting bosons: A functional renormalization group approach.

We calculate the temperature-dependent condensate density rho0(T) of interacting bosons in three dimensions using the functional renormalization group (FRG). From the numerical solution of suitably truncated FRG flow equations for the irreducible vertices we obtain rho0(T) for arbitrary temperatures. We carefully extrapolate our numerical results to the critical point and determine the order parameter exponent beta approximately 0.32 in reasonable agreement with the expected value 0.345 associated with the XY -universality class. We also calculate the condensate density in two dimensions at zero temperature using a truncation of the FRG flow equations based on the derivative expansion including cubic and quartic terms in the expansion of the effective potential in powers of the density. As compared with the widely used quadratic approximation for the effective potential, the coupling constants associated with the cubic and quartic terms lead to small corrections of the condensate density.

Absence of fermionic quasiparticles in the superfluid state of the attractive fermi gas.

We calculate the effect of order parameter fluctuations on the fermionic single-particle excitations in the superfluid state of neutral fermions interacting with short-range attractive forces. We show that in dimensions D< or =3 the singular effective interaction between the fermions mediated by the gapless Bogoliubov-Anderson mode prohibits the existence of well-defined quasiparticles. We explicitly calculate the single-particle spectral function in the BEC regime in D=3 and show that in this case the quasiparticle residue and the density of states are logarithmically suppressed.

Two-parameter scaling of correlation functions near continuous phase transitions.

We discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two-parameter scaling form G(k)=kc(-2)g(kxi,k/kc), where k is the wave vector and xi is the correlation length, and the interaction-dependent nonuniversal momentum scale kc remains finite at the critical fixed point. The correlation function describes the entire critical regime and captures the classical to critical crossover. One-parameter scaling is recovered only in the limit k/kc-->0. We present an approximate calculation of g(x,y) for the Ising universality class using the functional renormalization group.

Probing anomalous longitudinal fluctuations of the interacting Bose gas via Bose-Einstein condensation of magnons.

The emergence of a finite staggered magnetization in quantum Heisenberg antiferromagnets subject to a uniform magnetic field can be viewed as Bose-Einstein condensation of magnons. Using nonperturbative results for the infrared behavior of the interacting Bose gas, we present exact results for the staggered spin-spin correlation functions of quantum antiferromagnets in a magnetic field at zero temperature. In particular, we show that in dimensions 1

Persistent spin currents in mesoscopic Heisenberg rings.

We show that at low temperatures T an inhomogeneous radial magnetic field with magnitude B gives rise to a persistent magnetization current around a mesoscopic ferromagnetic Heisenberg ring. Under optimal conditions, this spin current can be as large as gmicro(B)(T/ variant Planck's over 2pi )exp([-2pi(gmicro(B)B/delta)(1/2)], as obtained from leading-order spin-wave theory. Here g is the gyromagnetic factor, micro(B) is the Bohr magneton, and delta is the energy gap between the ground-state and the first spin-wave excitation. The magnetization current endows the ring with an electric dipole moment.