Collective excitations and the crossover from Cooper pairs to composite bosons in the attractive Hubbard model

Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations

We present a method for computing the full probability distribution function of quadratic observables such as particle number or magnetization for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo calculations. Especially in cold atom experiments with single-site resolution, such a full counting statistics can be obtained from repeated projective measurements. We demonstrate that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find excellent agreement with recent experimental results. We show that current experiments are capable of probing the difference between the Hubbard model and the limiting Heisenberg model.

Signatures of fermion pairing with unconventional symmetry around the BCS-BEC crossover in a quasi-2D lattice

We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, d(x(2)-y(2)) and extended-s (s(*)), in the Bardeen-Cooper-Schrieffer-Bose-Einstein Condensation crossover region. We find that the fermion momentum distribution function, v(k)(2), the ratio of the Bogoliubov coefficients, v(k)/u(k), and the Fourier transform of v(k)(2) are strikingly different for d and s(*) symmetries in the crossover region. The chemical potential and the gap functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.

Entanglement and composite bosons

We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)10.1103/PhysRevA.71.034306] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity chi{N+1}/chi{N} that governs the bosonic character of a pair of fermions when N such pairs approximately share the same wave function. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity chi{N+1}/chi{N} approaches its ideal bosonic value.

Can one determine the underlying fermi surface in the superconducting state of strongly correlated systems?

The question of determining the underlying Fermi surface (FS) that is gapped by superconductivity (SC) is of central importance in strongly correlated systems, particularly in view of angle-resolved photoemission experiments. Here we explore various definitions of the FS in the superconducting state using the zero-energy Green's function, the excitation spectrum, and the momentum distribution. We examine (a) d-wave SC in high-Tc cuprates, and (b) the s-wave superfluid in the BCS-Bose-Einstein condensation (BEC) crossover. In each case we show that the various definitions agree, to a large extent, but all of them violate the Luttinger count and do not enclose the total electron density. We discuss the important role of chemical potential renormalization and incoherent spectral weight in this violation.

BCS-BEC crossover on the two-dimensional honeycomb lattice

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.