Particle-hole Fluctuations Research Articles

Anomalous dimers in quantum mixtures near broad resonances: Pauli blocking, Fermi surface dynamics, and implications

We study the energetics and dispersion of anomalous dimers that are induced by the Pauli blocking effect in a quantum Fermi gas of majority atoms near interspecies resonances. Unlike in vacuum, we find that both the sign and magnitude of the dimer masses are tunable via Feshbach resonances. We also investigate the effects of particle-hole fluctuations on the dispersion of dimers and demonstrate that the particle-hole fluctuations near a Fermi surface (with Fermi momentum $\ensuremath{\hbar}{k}_{F}$) generally reduce the effective two-body interactions and the binding energy of dimers. Furthermore, in the limit of light minority atoms the particle-hole fluctuations disfavor the formation of dimers with a total momentum $\ensuremath{\hbar}{k}_{F}$, because near $\ensuremath{\hbar}{k}_{F}$ the modes where the dominating particle-hole fluctuations appear are the softest. Our calculation suggests that near broad interspecies resonances when the minority-majority mass ratio ${m}_{B}/{m}_{F}$ is smaller than a critical value (estimated to be $0.136$), dimers in a finite-momentum channel are energetically favored over dimers in the zero-momentum channel. We apply our theory to quantum gases of $^{6}\mathrm{Li}$$^{40}\mathrm{K}$, $^{6}\mathrm{Li}$$^{87}\mathrm{Rb}$, $^{40}\mathrm{K}$$^{87}\mathrm{Rb}$, and $^{6}\mathrm{Li}$$^{23}\mathrm{Na}$ near broad interspecies resonances, and discuss the limitations of our calculations and implications.

Particle-hole fluctuations in BCS-BEC crossover

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the Gorkov effect and the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields ${T}_{c}/{T}_{F}=0.264$. We also investigate the crossover from broad to narrow Feshbach resonances---for the latter we obtain ${T}_{c}/{T}_{F}=0.204$ for ${a}^{\ensuremath{-}1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.

Magnetic properties ofYBa2Cu3O7−δin a self-consistent approach: Comparison with quantum Monte Carlo simulations and experiments

We analyze single-particle electronic and two-particle magnetic properties of the Hubbard model in the underdoped and optimally doped regime of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ by means of a modified version of the fluctuation-exchange approximation, which only includes particle-hole fluctuations. Comparison of our results with quantum--Monte Carlo (QMC) calculations at relatively high temperatures $(T\ensuremath{\sim}1000 \mathrm{K})$ suggests that we introduce a temperature renormalization in order to improve the agreement between the two methods at intermediate and large values of the interaction U. We evaluate the temperature dependence of the spin-lattice relaxation time ${T}_{1}$ and of the spin-echo decay time ${T}_{2G}$ and compare it with the results of NMR measurements on an underdoped and an optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ sample. For $U/t=4.5$ it is possible to consistently adjust the parameters of the Hubbard model in order to have a good semiquantitative description of this temperature dependence for temperatures larger than the spin gap as obtained from NMR measurements. We also discuss the case $U/t\ensuremath{\sim}8,$ which is more appropriate to describe magnetic and single-particle properties close to half filling. However, for this larger value of $U/t$ the agreement with QMC as well as with experiments at finite doping is less satisfactory.

Renormalization-group calculation for electrons in a half-filled Landau level.

The major obstacle for analytic calculations for electrons in the lowest Landau level arises from the degeneracy of the single-particle eigenstates. When the electron-electron interaction is included, the diagonal energy of different basis states is no longer the same and degenerate perturbation theory can be carried out. The near degeneracy of the single-particle states is manifested as an infrared-divergent perturbation series which is similar to that of a collection of one-dimensional interacting spinless chains. Thus a renormalization-group scheme can be developed. The range of the interparticle potential affects the change in diagonal energy for particle-hole fluctuations. For the Coulomb potential we find that the coupling constants remain unchanged over many length scales. The system remains gapless, consistent with recent transport and surface-acoustic-wave measurements.

Quasi-superconductivity in one-dimensional conductor

An enhancement of a Cooper pair vertex part by a particle-hole density fluctuation in one dimensional conductors at low temperature yields a higher superconductive transition temperature T(1)c over the three dimensional T(3)c for the threads of linear conductors, between which there are couplings such as to yield T(3)c.