A variational theory of fermion matter with spin dependent correlations

Rakhal Deviprasad Dave

George Kastrinakis

We introduce a new fermionic variational wavefunction, generalizing the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which is suitable for interacting multi-species spinful systems and sustaining superfluidity. Applications range from quark matter to the high temperature superconductors. A wide class of Hamiltonians, comprising interactions and hybridization of arbitrary momentum dependence between different fermion species, can be treated in a comprehensive manner. This is the case, as both the intra-species and the inter-species interactions are treated on equally rigorous footing, which is accomplished via the introduction of a new quantum index attached to the fermions. The index is consistent with known fermionic physics, and allows for heretofore unaccounted for fermion-fermion correlations. We have derived the finite temperature version of the theory, thus obtaining the renormalized quasiparticle dispersion relations, and we discuss the appearance of charge and spin density wave order. We present numerical solutions for two electron species in 2 dimensions. Based on these solutions, we show that, for equivalent spin up and down fermions, the Fermi occupation factor (per spin) equals 1/2 deep in the Fermi sea. This constitutes a unique experimental prediction of the theory, both for the normal and superfluid states. Interestingly, this result, obtained in the thermodynamic limit, is consistent with Fermi occupation factor (in-)equalities for finite systems of electrons, derived (in a different context) by Borland and Dennis, J. Phys. B {\bf 5}, 7 (1972) and by Altunbulak and Klyachko, Commun. Math. Phys. {\bf 282}, 287 (2008).

Christina V. Kraus

Quantum correlations in fermionic system are central to many fascinating effects in condensed matter physics. In this Thesis we investigate these correlations from the perspective of quantum information theory. Motivated by recent experiments on ultra cold gases, we develop a “pairing theory” for fermionic systems. Next, we investigate possibilities to gain insight into the correlations of these systems using simulation techniques. On the one hand, we study the power of quantum systems for the simulation of fermionic, bosonic and spin systems. On the other hand, we develop numerical methods applicable to interacting fermionic systems. First, we construct a class of variational states well suited for the approximation of ground and thermal states of systems with short-range interaction. Then, we develop a method that allows the numerical approximation of observables in dynamical processes as well as in equilibrium.

Walter Metzner

C Howes, J M Irvine, R. F. Bishop

Bethe (1973) has proposed two model N-N interactions, one containing a central plus sigma 1 . sigma 2 spin dependence and the other containing in addition a tensor force to study the convergence of various many-body techniques for calculating the bulk properties of many fermion fluids. Following the success of the authors' constrained variational calculations in describing the behaviour of the original Bethe homework problem involving a purely central interaction, they now present their results in neutron matter and nuclear matter for the new spin-dependent potentials.

Виктор Павлович Маслов