Stefan M. A. Rombouts

Exactly-solvable models derived from a generalized Gaudin algebra

Abstract We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different representations of the generators of the algebra. The derived exactly-solvable generalized Gaudin models include the Hamiltonians of Bardeen–Cooper–Schrieffer, Suhl–Matthias–Walker, Lipkin–Meshkov–Glick, the generalized Dicke and atom–molecule, the nuclear interacting boson model, a new exactly-solvable Kondo-like impurity model, and many more that have not been exploited in the physics literature yet.

Quantum phase diagram of the integrable px+ipy fermionic superfluid

eld solution allows to connect these results to other models with px + ipy pairing order. We dene an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a connementdeconnement type without local order parameter. We show that this phase transition is not limited to the px +ipy pairing model, but can be found in any representation of the hyperbolic RichardsonGaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.

Quantum phase diagram of the integrablepx+ipyfermionic superfluid

eld solution allows to connect these results to other models with px + ipy pairing order. We dene an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a connementdeconnement type without local order parameter. We show that this phase transition is not limited to the px +ipy pairing model, but can be found in any representation of the hyperbolic RichardsonGaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.

Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices.

The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.

Engineering local optimality in quantum Monte Carlo algorithms

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and can have a winding number larger than zero. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.

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.

Integrable two-channel px+ipy-wave model of a superfluid

We present a new two-channel integrable model describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the pwave model has a third order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact manybody wavefunction provides a unique perspective of the quantum critical region suggesting that the size of the condensate wavefunction, that diverges logarithmically with the chemical potential, could be used as an experimental indicator of the phase transition.

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.