Nils Hasselmann

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.

Self-energy and critical temperature of weakly interacting bosons

Using the exact renormalization group we calculate the momentum-dependent self-energy {sigma}(k) at zero frequency of weakly interacting bosons at the critical temperature T{sub c} of Bose-Einstein condensation in dimensions 3{ 3 and {sigma}(k){proportional_to}ln(k/k{sub c}) in D=3. Our approach yields the crossover scale k{sub c} on the same footing with a reasonable estimate for the critical exponent {eta} in D=3. From our {sigma}(k) we find for the interaction-induced shift of T{sub c} in three dimensions {delta}T{sub c}/T{sub c}{approx_equal}1.23an{sup 1/3}, where a is the s-wave scattering length and n is the density.

Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

We include spontaneous symmetry breaking in the functional renormalization group equations for the irreducible vertices of Ginzburg–Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each renormalization group (RG) step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Σ(k) and interpolates between lowest-order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Σ(k) = kc2σ−(|k|ξ,|k|/kc), where ξ is the order parameter correlation length, kc is the Ginzburg scale, and σ−(x,y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we calculate explicitly within our truncation.

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.

Quantum Heisenberg antiferromagnets in a uniform magnetic field : Nonanalytic magnetic field dependence of the magnon spectrum

We reexamine the

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

1/S

Spin-wave interactions in quantum antiferromagnets

correction to the self-energy of the gapless magnon of a

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

D

Functional renormalization group approach to the two dimensional Bose gas

-dimensional quantum Heisenberg antiferromagnet in a uniform magnetic field

Effective spin-wave action for ordered Heisenberg antiferromagnets in a magnetic field

h