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Register a new userPhase space analysis of interacting fermions
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M. Ossadnik
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We propose the use of an orthogonal wave packet basis to analyze the low-energy physics of interacting electron systems with short range order. We give an introduction to wave packets and the related phase space representation of fermion systems, and show that they lend themselves to an efficient description of short range order. We illustrate the approach within an RG calculation for the one-dimensional Hubbard chain.
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We apply Dynamical Mean-Field Theory to strongly interacting fermions in an inhomogeneous environment. With the help of this Real-Space Dynamical Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin 1/2 in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.
This review is a summary of my work (partially in collaboration with Kurt Schoenhammer) on higher-dimensional bosonization during the years 1994-1996. It has been published as a book entitled Bosonization of interacting fermions in arbitrary dimensions by Springer Verlag (Lecture Notes in Physics m48, Springer, Berlin, 1997). I have NOT revised this review, so that there is no reference to the literature after 1996. However, the basic ideas underlying the functional bosonization approach outlined in this review are still valid today.
We present a formalism to calculate the orbital magnetization of interacting Dirac fermions under a magnetic field. In this approach, the divergence difficulty is overcome with a special limit of the derivative of the thermodynamic potential with respect to the magnetic field. The formalism satisfies the particle-hole symmetry of the Dirac fermions system. We apply the formalism to the interacting Dirac fermions in graphene. The charge and spin orderings and the exchange interactions between all the Landau levels are taken into account by the mean-field theory. The results for the orbital magnetization of interacting Dirac fermions are compared with that of non-interacting cases.
In this thesis, we study the breakdown of the Fermi liquid state in cuprate superconductors using the renormalization group (RG). We seek to extend earlier work on the crossover from the Fermi liquid state to the pseudo gap phase based on RG flows in the so-called saddle point regime. Progress in the derivation of effective models for the conjectured spin liquid state has been hindered, by the difficulties involved in solving the strong coupling low energy Hamiltonian. We tackle the problem by introducing an orthogonal wave packet basis, the so-called Wilson-Wannier (WW) basis, that can be used to interpolate between the momentum space and the real space descriptions. We show how to combine the WW basis with the RG, such that the RG is used to eliminate high-energy degrees of freedom, and the remaining strongly correlated system is solved approximately in the WW basis. We exemplify the approach for different one-dimensional model systems, and find good qualitative agreement with exact solutions even for very simple approximations. Finally, we reinvestigate the saddle point regime of the two-dimensional Hubbard model. We show that the anti-nodal states are driven to an insulating spin-liquid state with strong singlet pairing correlations, thus corroborating earlier conjectures.
Interacting spinning fermions with strong quasi-random disorder are analyzed via rigorous Renormalization Group (RG) methods combined with KAM techniques. The correlations are written in terms of an expansion whose convergence follows from number-theoretical properties of the frequency and cancellations due to Pauli principle. A striking difference appears between spinless and spinning fermions; in the first case there are no relevant effective interactions while in presence of spin an additional relevant quartic term is present in the RG flow. The large distance exponential decay of the correlations present in the non interacting case, consequence of the single particle localization, is shown to persist in the spinning case only for temperatures greater than a power of the many body interaction, while in the spinless case this happens up to zero temperature.
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