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.

We investigate the single-particle spectral density of interacting bosons within the non-perturbative functional renormalization group technique. The flow equations for a Bose gas are derived in a scheme which treats the two-particle density-density correlations exactly but neglects irreducible correlations among three and more particles. These flow equations are solved within a truncation which allows to extract the complete frequency and momentum structure of the normal and anomalous self-energies. Both the asymptotic small momentum regime, where perturbation regime fails, as well as the perturbative regime at larger momenta are well described within a single unified approach. The self-energies do not exhibit any infrared divergences, satisfy the U (1) symmetry constraints, and are in accordance with the Nepomnyashchy relation which states that the anomalous self-energy vanishes at zero momentum and zero frequency. From the self-energies we extract the single-particle spectral density of the two-dimensional Bose gas. The dispersion is found to be of the Bogoliubov form and shows the crossover from linear Goldstone modes to the quadratic behavior of quasi-free bosons. The damping of the quasiparticles is found to be in accordance with the standard Beliaev damping. We furthermore recover the exact asymptotic limit of the propagators derived by Gavoret and Nozières and discuss the nature of the non-analyticities of the self-energies in the very small momentum regime.

We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic singularity appears in the Hall conductivity when the frequency of the external field agrees with the width of the gap.

We discuss the statistics of Bose-Einstein condensation (BEC) in a canonical ensemble of N noninteracting bosons in terms of a Landau function L BEC N (q) defined by the logarithm of the probability distribution of the order parameter q for BEC. We also discuss the corresponding Landau function for spontaneous symmetry breaking (SSB), which for finite N should be distinguished from L BEC N (q). Only for N → ∞ BEC and SSB can be described by the same Landau function which depends on the dimensionality and on the form of the external potential in a surprisingly complex manner. For bosons confined by a three-dimensional harmonic trap the Landau function exhibits the usual behavior expected for continuous phase transitions.The concept of a Landau function L(p) has been extremely useful to understand the nature of phase transitions [1]. For example, in the vicinity of a second order (continuous) thermal phase transition L(p) smoothly develops minima at non-zero values of the relevant order parameter p when the temperature T drops below the critical temperature T c , see Fig. 1 (a). On the other hand, in the case of a first order phase transition the location of the minima of L(p) changes discontinuously at T = T c , as shown in Fig. 1(b). While for infinite systems and in the absence of spontaneous symmetry breaking (SSB) L(p) can be identified with the Gibbs potential, this identification is in general not valid for finite systems or in the symmetry broken phase. In the latter case the Gibbs potential, which by construction is a convex function of p, exhibits a plateau as shown in Fig. 1. Microscopically, L(p) is defined in terms of the logarithm of the probability distribution of the order parameter in a given statistical ensemble [1]. From this probabilistic definition it is clear that L(p) does not have a strictly thermodynamic interpretation.For non-interacting systems the Landau function is in (b) (a) rag replacements T > Tc T = Tc T < Tc p L FIG. 1: Typical evolution of the Landau function L as a function of the relevant order parameter p close to (a) second order and (b) first order phase transitions. The dashed line denotes the plateau of the corresponding Gibbs potential for T < Tc.most cases not very interesting, because the correlations responsible for phase transitions are usually due to interactions between the microscopic degrees of freedom. An important exception are non-interacting bosons, where at low temperatures the correlations imposed by quantum statistics are sufficient to give rise to a phase transition, the Bose-Einstein condensation (BEC) [2,3]. In the condensed state the fraction of particles that occupy the single-particle state with the lowest energy is of the order of unity. More precisely, the order parameter for BEC can be chosen to be the expectation value of the operatorq = b † 0 b 0 /N , where b 0 annihilates a boson in the single-particle ground state and N is the total number of particles in the system.Conceptually, BEC should be distinguished from SSB, which manifests itself via a...

We study the effect of interlayer Coulomb interaction in an electronic double layer. Assuming that each of the layers consists of a bipartite lattice, a sufficiently strong interlayer interaction leads to an interlayer pairing of electrons with a staggered order parameter. We show that the correlated pairing state is dual to the excitonic pairing state with a uniform order parameter in an electron-hole double layer. The interlayer pairing of electrons leads to strong current-current correlations between the layers. We also analyze the interlayer conductivity and the fluctuations of the order parameter, which consists of a gapped and a gapless mode.

We investigate the scaling properties of the recently acquired fermionic nonlinear σ model which controls gapless diffusive modes in a two-dimensional disordered system of Dirac electrons beyond charge neutrality. The transport on large scales is governed by a renormalizable nonlocal field theory. For zero-mean random gap, it is characterized by the absence of a dynamic gap generation and a scale-invariant diffusion coefficient. The β function of the dc conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.

The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. Here we consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band structure on the optical conductivity and on diffusion due to quantum fluctuations. In contrast to the behavior at an isotropic node we find super-and subdiffusion for the anisotropic node. The spectral saddle points create van Hove singularities in the optical conductivity, which could be used to characterize the spectral properties experimentally.

We study the influence of lattice deformations on the optical conductivity of a two-dimensional electron gas. Lattice deformations are taken into account by introducing a non-abelian gauge field into the Eucledian action of two-dimensional Dirac electrons. This is in analogy to the introduction of the gravitation in the four-dimensional quantum field theory. We examine the effect of these deformations on the averaged optical conductivity. Within the perturbative theory up to second order we show that corrections of the conductivity due to the deformations cancel each other exactly. We argue that these corrections vanish to any order in perturbative expansion.