Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems

Masanori Yamanaka, Yasuhiro Hatsugai, Mahito Kohmoto

Alex Kamenev

Lecture notes presented at Windsor NATO school on "Field Theory of Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems" (August 2001). The purpose of these lectures is to give a brief modern introduction to Keldysh non-equilibrium field theory and its classical analog - Doi-Peliti technique. The special emphasis is put on stressing the analogy between the two approaches.

Philippe Corboz

Jiann-Feng Jan

Laurent Sanchez-Palencia, V. Ahufinger, Adrian Kantian +3 more

We investigate theoretically the low-temperature physics of a two-component ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson-boson and the boson-fermion interactions, the tunneling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and we show that it corresponds to the formation of Fermi glasses, spin glasses, and quantum percolation regimes.

Dimitri M. Gangardt

We calculate the asymptotic behaviour of the one body density matrix of one-dimensional impenetrable bosons in finite size geometries. Our approach is based on a modification of the Replica Method from the theory of disordered systems. We obtain explicit expressions for oscillating terms, similar to fermionic Friedel oscillations. These terms are universal and originate from the strong short-range correlations between bosons in one dimension.