arXiv subjects
Publications and source records attributed to Pierbiagio Pieri.
We discuss how approximate theories for Bose-Fermi mixtures recover in the molecular limit the expected expression for Fermi-Fermi mixtures of molecules and unpaired fermions. In particular, we compare the energy of the system resulting from a T-matrix diagrammatic approach with that obtained with Variational and Fixed-Node Diffusion Quantum Monte Carlo methods.
We calculate the single-particle spectral functions and quasi-particle dispersions for a Bose-Fermi mixture when the boson-fermion attraction is sufficiently strong to suppress completely the condensation of bosons at zero temperature. Within a T-matrix diagrammatic approach, we vary the boson-fermion attraction from the critical value where the boson condensate first disappears to the strongly attractive (molecular) regime and study the effect of both mass- and density-imbalance on the spectral weights and dispersions. An interesting spectrum of particle-hole excitations mixing two different Fermi surfaces is found. These unconventional excitations could be produced and explored experimentally with radio-frequency spectroscopy.
The Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS to BEC) crossover problem is solved for stationary grey solitons via the Boguliubov-de Gennes equations at zero temperature. These \emph{crossover solitons} exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitary the velocity has a nearly linear dependence on phase difference over an extended range. For fixed phase difference the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power law relationship to express this fact: the density of grey crossover solitons varies as the square of the gap amplitude in the BEC limit and a power of about 1.5 at unitarity.
We study by diagrammatic methods a mixture of single-component bosons and fermions, with boson-fermion coupling tuned by a Fano-Feshbach resonance. For increasing coupling, the growing boson-fermion pairing correlations progressively reduce the boson condensation temperature and make it eventually vanish at a critical coupling. Such quantum critical point depends very weakly on the population imbalance and for vanishing boson densities coincides with that found for the polaron-molecule transition in a strongly imbalanced Fermi gas, thus bridging two quite distinct physical systems.
Ultracold Fermi atoms allow the realization of the crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose- Einstein condensation (BEC), by varying with continuity the attraction between fermions of different species. In this context, radio frequency (RF) spectroscopy provides a microscopic probe to infer the nature of fermionic pairing. In the strongly-interacting regime, this pairing affects a wide temperature range comprising the critical temperature T_c, in analogy to the pseudogap physics for high-temperature superconductors. By including what are known in superconductors as "paraconductivity" fluctuations, here we calculate the RF spectra above T_c for fermions with balanced populations and compare them with available experimental data, thus revealing that the role of these fluctuations is considerably enhanced with respect to superconductors. In addition, we extract from the spectra an energy scale associated with pairing and relate it to a universal quantity recently introduced for Fermi gases.
We present in this paper a nonlinear sigma-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a novel calculation, at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a stedily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical (DMRG) status of the art as well as with previous analytical approaches is also made.
We present here a nonlinear sigma-model (NL$σ$M) study of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. We find, already at the mean-field level, excellent agreement with recent and very accurate Density Matrix Renormalization Group (DMRG) studies, and that up to the highest values of the field for which a comparison is possible, for the staggered magnetization and the transverse spin gap. Qualitative but not quantitative agreement is found between the NL$σ$M predictions for the longitudinal spin gap and the DMRG results. The origin of the discrepancies is traced and discussed. Our results allow for extensions to higher-spin chains that have not yet been studied numerically, and the predictions for a spin-2 chain are presented and discussed. Comparison is also made with previous theoretical approaches that led instead to predictions in disagreement with the DMRG results.
We study the t-J model with the inclusion of the so called three-site term which comes out from the t/U --> 0 expansion of the Hubbard model. We find that this singlet pair hopping term has no qualitative effect on the structure of the pure mean field phase diagram for nonmagnetic states. In accordance with experimental data on high-T_c materials and some numerical studies, we also find wide regions of phase coexistence whenever the coupling J is greater than a critical value J_c. We show that J_c varies linearly with the temperature T, going to zero at T=0.
We study the so-called nonmagnetic phases (dimer and flux states) in the t-J model below half filling. We present a new phase diagram, at zero and finite temperature, that includes broad areas of phase coexistence (dimer-flux or flux-uniform), in accordance with experimental and numerical data on the possibility of separation into hole-rich and hole-poor regions. We also briefly comment on some techniques used in the literature to discuss phase separation in the t-J model.