scholarly journals Self-consistent study of Anderson localization in the Anderson-Hubbard model in two and three dimensions

2008 ◽  
Vol 78 (23) ◽  
Author(s):  
Peter Henseler ◽  
Johann Kroha ◽  
Boris Shapiro
Keyword(s):  
Hubbard Model ◽  
Anderson Localization ◽  
Three Dimensions ◽  
Self Consistent

scholarly journals Anderson localization effects on the doped Hubbard model

2021 ◽  
Vol 103 (24) ◽  
Author(s):  
Nathan Giovanni ◽  
Marcello Civelli ◽  
Maria C. O. Aguiar
Keyword(s):  
Hubbard Model ◽  
Anderson Localization

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals Self-Consistent Calculation of Particle-Hole Diagrams on the Matsubara Frequency: Flex Approximation

1997 ◽  
Vol 08 (05) ◽  
pp. 1145-1158
Author(s):  
J. J. Rodríguez-Núñez ◽  
S. Schafroth
Keyword(s):  
Hubbard Model ◽  
Imaginary Part ◽  
Chemical Potential ◽  
Order Approximation ◽  
The Self ◽  
Green Functions ◽  
Matsubara Frequency ◽  
Self Energy ◽  
Peak Structure ◽  
Self Consistent

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling (ρ =0.40), and for T/t = 0.03, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im Σ( k , ω) ≈ w2 around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully self-consistent and the non-self-consistent ones give different results for the parameters considered here. However, they have similar global results for small densities.

scholarly journals Antiferromagnetism in the Hubbard model on the honeycomb lattice: A two-particle self-consistent study

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
S. Arya ◽  
P. V. Sriluckshmy ◽  
S. R. Hassan ◽  
A.-M. S. Tremblay
Keyword(s):  
Hubbard Model ◽  
Honeycomb Lattice ◽  
Self Consistent

ANDERSON LOCALIZATION IN THE SEVENTIES AND BEYOND

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1507-1525 ◽  
Author(s):  
David Thouless
Keyword(s):  
Quantum Hall Effect ◽  
Anderson Localization ◽  
Quantum Hall ◽  
Experimental Tests ◽  
Three Dimensions ◽  
Electronic Systems ◽  
Atomic Systems ◽  
One Dimensional ◽  
Extended States ◽  
Energy States

Little attention was paid to Anderson's challenging paper on localization for the first ten years, but from 1968 onwards it generated a lot of interest. Around that time a number of important questions were raised by the community, on matters such as the existence of a sharp distinction between localized and extended states, or between conductors and insulators. For some of these questions the answers are unambiguous. There certainly are energy ranges in which states are exponentially localized, in the presence of a static disordered potential. In a weakly disordered one-dimensional potential, all states are localized. There is clear evidence, in three dimensions, for energy ranges in which states are extended, and ranges in which they are diffusive. Magnetic and spin-dependent interactions play an important part in reducing localization effects. For massive particles like electrons and atoms the lowest energy states are localized, but for massless particles like photons and acoustic phonons the lowest energy states are extended. Uncertainties remain. Scaling theory suggests that in two-dimensional systems all states are weakly localized, and that there is no minimum metallic conductivity. The interplay between disorder and mutual interactions is still an area of uncertainty, which is very important for electronic systems. Optical and dilute atomic systems provide experimental tests which allow interaction to be much less important. The quantum Hall effect provided a system where states on the Fermi surface are localized, but non-dissipative currents flow in response to an electric field.

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