K. Van Houcke

Diagrammatic Monte Carlo for correlated fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynmans diagrammatic series for the single-particle self-energy, we can study moderate values of the on-site repulsion (U/t~4) and temperatures down to T/t=1/40. We compare our results with high-temperature series expansions and with single-site and cluster dynamical mean-field theory.

Loop updates for quantum Monte Carlo simulations in the canonical ensemble.

We present a new nonlocal updating scheme for quantum Monte Carlo simulations, which conserves particle number and other symmetries. It allows exact symmetry projection and direct evaluation of the equal-time Greens function and other observables in the canonical ensemble. The method is applicable to a wide variety of systems. We show results for bosonic atoms in optical lattices, neutron pairs in atomic nuclei, and electron pairs in ultrasmall superconducting grains.

Integrable Models for Asymmetric Fermi Superfluids: Emergence of a New Exotic Pairing Phase

We introduce an exactly solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair excitations. It is proven that this phase is the exact ground state in the strong-coupling limit, while numerical examples in finite lattices show that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.

Quantum Monte Carlo simulation in the canonical ensemble at finite temperature.

A quantum Monte Carlo method with a nonlocal update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and respects other exact symmetries. Observables like the equal-time Greens function can be evaluated in an efficient way. To demonstrate the versatility of the method, results for the one-dimensional Bose-Hubbard model and a nuclear pairing model are presented. Within the context of the Bose-Hubbard model the efficiency of the algorithm is discussed.

Survival of parity effects in superconducting grains at finite temperature

We study the thermodynamics of a small, isolated superconducting grain using a recently developed quantum Monte Carlo method. This method allows us to simulate grains at any finite temperature and with any level spacing in an exact way. We focus on the pairing energy, pairing gap, condensation energy, heat capacity, and spin susceptibility to describe the grain. We discuss the interplay between finite size (mesoscopic system), pairing correlations, and temperature in full detail.

Effect of a Zeeman field on the transition from superconductivity to ferromagnetism in metallic grains

We investigate the competition between pairing correlations and ferromagnetism in small metallic grains in the presence of a Zeeman field. Our analysis is based on the universal Hamiltonian, valid in the limit of large Thouless conductance. We show that the coexistence regime of superconducting and ferromagnetic correlations can be made experimentally accessible by tuning an external Zeeman field. We compare the exact solution of the model with a mean-field theory and find that the latter cannot describe pairing correlations in the intermediate regime. We also study the occurrence of spin jumps across the phase boundary separating the superconducting and coexistence regimes.We investigate the competition between pairing correlations and ferromagnetism in small metallic grains in the presence of a Zeeman field. Our analysis is based on the universal Hamiltonian, valid in the limit of large Thouless conductance. We show that the coexistence regime of superconducting and ferromagnetic correlations can be made experimentally accessible by tuning an external Zeeman field. We compare the exact solution of the model with a mean-field theory and find that the latter cannot describe pairing correlations in the intermediate regime. We also study the occurrence of spin jumps across the phase boundary separating the superconducting and coexistence regimes.

Microscopic calculation of symmetry projected nuclear level densities

We present a quantum Monte Carlo method with exact projection on parity and angular momentum that is free of a sign problem for seniority-conserving nuclear interactions. This technique allows the microscopic calculation of angular momentum and parity-projected nuclear level densities. We present results for the {sup 55}Fe, {sup 56}Fe, and {sup 57}Fe isotopes. Signatures of the pairing phase transition are observed in the angular momentum distribution of the nuclear level density.