Fermi gas response to time-dependent perturbations

We describe the Riemann-Hilbert (RH) approach to computing the long-time response of a Fermi gas to a time-dependent perturbation. The approach maps the problem onto a non-commuting RH problem. The method is non-perturbative, quite general and can be used to compute the Fermi gas response in driven (out of equilibrium) as well as equilibrium systems. We illustrate the power of the method by rederiving standard results for the core-hole and open-line Greens functions for the equilibrium Fermi edge singularity (FES) problem. We then show that the case of the non-separable potential can be solved non-perturbatively with no more effort than for the separable case. We compute the corresponding results for a biased (non-equilibrium) model tunneling device, similar to those used in single photon detectors, in which a photon absorption process can significantly change the conductance of the barrier. For times much larger than the inverse bias across the device, the response of the Fermi gases in the two electrodes shows that the equilibrium Fermi edge singularity is smoothed, shifted in frequency and becomes polarity-dependent.These results have a simple interpretation in terms of known results for the equilibrium case but with (in general complex-valued) combinations of elements of the scattering matrix replacing the equilibrium phase shifts. We also consider the shot noise spectrum of a tunnel junction subject to a time-dependent bias and demonstrate that the calculation is essentially the same as for the FES problem. For the case of a periodically driven device we show that the noise spectrum for the Coherent States of Alternating Current can be easily obtained using this approach.Comment: 15 page

Breakdown of Migdal--Eliashberg theory via catastrophic vertex divergence at low phonon frequency

We investigate the applicability of Migdal--Eliashberg (ME) theory by revisiting Migdal's analysis within the dynamical mean-field theory framework. First, we compute spectral functions, the quasi-particle weight, the self energy, renormalised phonon frequency and resistivity curves of the half-filled Holstein model. We demonstrate how ME theory has a phase-transition-like instability at intermediate coupling, and how the Engelsberg--Schrieffer (ES) picture is complicated by low-energy excitations from higher order diagrams (demonstrating that ES theory is a very weak coupling approach). Through consideration of the lowest-order vertex correction, we analyse the applicability of ME theory close to this transition. We find a breakdown of the theory in the intermediate coupling adiabatic limit due to a divergence in the vertex function. The region of applicability is mapped out, and it is found that ME theory is only reliable in the weak coupling adiabatic limit, raising questions about the accuracy of recent analyses of cuprate superconductors which do not include vertex corrections.Comment: 19 pages, 10 figures, accepted for publication in Journal of Low Temperature Physic

Bosonization for 2D Interacting Fermion Systems: Non-Fermi Liquid Behavior

Non-Fermi liquid behavior is found for the first time in a two-dimensional (2D) system with non-singular interactions using Haldane's bosonization scheme. The bosonized system is solved exactly by a generalized Bogoliubov transformation. The fermion momentum distribution, calculated using a generalized Mattis-Lieb technique, exhibits a non-universal power law in the vicinity of the Fermi surface for intermediate interaction strengths.Comment: 13 pages, 2 figures upon request, latex. (to appear in Mod. Phys. Lett. B

Search for electron liquids with non-Abelian quasiparticles

We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors $7/3 <\nu_e<8/3$. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at $\nu_e=5/2$ (paired Moore--Read "pfafian" state) and 12/5 (clustered Read--Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline $\nu_e=7/3$ state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.Comment: 9 pages, 8 figure

Tuning Correlation Effects with Electron–Phonon Interactions

We investigate the effect of tuning the phonon energy on the correlation effects in models of electron–phonon interactions using DMFT. In the regime where itinerant electrons, instantaneous electron–phonon driven correlations and static distortions compete on similar energy scales, we find several interesting results including (1) A crossover from band to Mott behavior in the spectral function, leading to hybrid band/Mott features in the spectral function for phonon frequencies slightly larger than the band width. (2) Since the optical conductivity depends sensitively on the form of the spectral function, we show that such a regime should be observable through the low frequency form of the optical conductivity. (3) The resistivity has a double kondo peak arrangement

Probing short-range magnetic order in a geometrically frustrated magnet by spin Seebeck effect

Competing magnetic interactions in geometrically frustrated magnets give rise to new forms of correlated matter, such as spin liquids and spin ices. Characterizing the magnetic structure of these states has been difficult due to the absence of long-range order. Here, we demonstrate that the spin Seebeck effect (SSE) is a sensitive probe of magnetic short-range order (SRO) in geometrically frustrated magnets. In low temperature (2 - 5 K) SSE measurements on a model frustrated magnet \mathrm{Gd_{3}Ga_{5}O_{12}}, we observe modulations in the spin current on top of a smooth background. By comparing to existing neutron diffraction data, we find that these modulations arise from field-induced magnetic ordering that is short-range in nature. The observed SRO is anisotropic with the direction of applied field, which is verified by theoretical calculation.Comment: 5 pages, 4 figure

Transition from quantum Hall to compressible states in the second Landau level: new light on the ν\nu=5/2 enigma

Quantum Hall states at filling fraction $\nu$=5/2 are examined by numerical diagonalization. Spin-polarized and -unpolarized states of systems with $N\le 18$ electrons are studied, neglecting effects of Landau level mixing. We find that the ground state is spin polarized. It is incompressible and has a large overlap with paired states like the Pfaffian. For a given sample, the energy gap is about 11 times smaller than at $\nu$=1/3. Evidence is presented of phase transitions to compressible states, driven by the interaction strength at short distance. A reinterpretation of experiments is suggested.Comment: This paper has already appeared in PRL, but has not been on the we

Stability and effective masses of composite-fermions in the first and second Landau Level

We propose a measure of the stability of composite fermions (CF's) at even-denominator Landau-level filling fractions. Assuming Landau-level mixing effects are not strong, we show that the CF liquid at $\nu=2+1/2$ in the $n=1$ Landau level cannot exist and relate this to the absence of a hierarchy of incompressible states for filling fractions $2+1/3 < \nu < 2+2/3$. We find that a polarized CF liquid should exist at $\nu=2+1/4$. We also show that, for CF states, the variation with system size of the ground state energy of interacting electrons follows that for non-interacting particles in zero magnetic field. We use this to estimate the CF effective masses.Comment: 9 pages, Revtex, PSIZ-TP-940

Interaction dependence of composite fermion effective masses

We estimate the composite fermion effective mass for a general two particle potential r^{-\alpha} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction \nu=1/2 as well as estimates of the excitation gap at \nu=1/3, 2/5 and 3/7 show that m_eff \sim \alpha^{-1}.Comment: 4 pages, RevTeX, 5 figure