13,699 research outputs found
A Large Deviation Rate and Central Limit Theorem for Horton Ratios
Although originating in hydrology, the classical Horton analysis is based on a geometric progression that is widely used in the empirical analysis of branching patterns found in biology, atmospheric science, plant pathology, etc., and more recently in tree register allocation in computer science. The main results of this paper are a large deviation rate and a central limit theorem for Horton bifurcation ratios in a standard network model. The methods are largely self-contained. In particular, derivations of some previously known results of the theory are indicated along the way
Interaction induced topological phase transition in Bernevig-Hughes-Zhang model
We study interaction induced topological phase transition in
Bernevig-Hughes-Zhang model. Topological nature of the phase transition is
revealed by directly calculating the Z2 index of the interacting system from
the single-particle Green's function. The interacting Z2 index is also
consistently checked through the edge spectra. Combined with ab initio methods,
present approach is a useful tool searching for correlated topological
insulating materials from the first-principle point of view.Comment: 4.5 pages, 4 figures, reference adde
Pole expansion of self-energy and interaction effect on topological insulators
We study effect of interactions on time-reversal-invariant topological
insulators. Their topological indices are expressed by interacting Green's
functions. Under the local self-energy approximation, we connect topological
index and surface states of an interacting system to an auxiliary
noninteracting system, whose Hamiltonian is related to the pole-expansions of
the local self-energy. This finding greatly simplifies the calculation of
interacting topological indices and gives an noninteracting pictorial
description of interaction driven topological phase transitions. Our results
also bridge studies of the correlated topological insulating materials with the
practical dynamical-mean-field-theory calculations.Comment: 4.2 pages, 3 figures, reference added, typos correcte
Magnetism of Cold Fermionic Atoms on p-Band of an Optical Lattice
We carry out \textit{ab initio} study of ground state phase diagram of
spin-1/2 cold fermionic atoms within two-fold degenerate -band of an
anisotropic optical lattice. Using the Gutzwiller variational approach, we show
that a robust ferromagnetic phase exists for a vast range of band fillings and
interacting strengths. The ground state crosses over from spin density wave
state to spin-1 Neel state at half filling. Additional harmonic trap will
induce spatial separation of varies phases. We also discuss several relevant
observable consequences and detection methods. Experimental test of the results
reported here may shed some light on the long-standing issue of itinerant
ferromagnetism.Comment: 5 pages, 4 figure
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