scholarly journals Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

2014 ◽  
Vol 89 (8) ◽  
Author(s):  
C. E. Ekuma ◽  
H. Terletska ◽  
K.-M. Tam ◽  
Z.-Y. Meng ◽  
J. Moreno ◽  
...  
Keyword(s):  
Anderson Localization ◽  
Three Dimensions ◽  
Cluster Approximation ◽  
Dynamical Cluster Approximation

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.

scholarly journals Mottness collapse and statistical quantum criticality

2011 ◽  
Vol 369 (1941) ◽  
pp. 1599-1625 ◽  
Author(s):  
J. Zaanen ◽  
B. J. Overbosch
Keyword(s):  
Scale Invariance ◽  
Quantum Dynamics ◽  
Cuprate Superconductors ◽  
Quantum Criticality ◽  
Cluster Approximation ◽  
Integral Formalism ◽  
Model Sets ◽  
Sign Structure ◽  
Normal Fermi ◽  
Dynamical Cluster Approximation

We put forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness, as advocated by Phillips and supported by recent dynamical cluster approximation results on the Hubbard model, sets the necessary microscopic conditions. The crucial insight is due to Weng, who demonstrated that, in the presence of Mottness, the fundamental workings of quantum statistics change, and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing it further using numerical methods. The pseudo-gap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi–Dirac statistics. Proof of principle follows from Ceperley’s constrained path integral formalism, in which states can be explicitly constructed showing a merger of Fermi–Dirac sign structure and scale invariance of the quantum dynamics.

scholarly journals Study of multiband disordered systems using the typical medium dynamical cluster approximation

2015 ◽  
Vol 92 (20) ◽  
Author(s):  
Yi Zhang ◽  
Hanna Terletska ◽  
C. Moore ◽  
Chinedu Ekuma ◽  
Ka-Ming Tam ◽  
...  
Keyword(s):  
Disordered Systems ◽  
Cluster Approximation ◽  
Dynamical Cluster Approximation

scholarly journals Mott transition in the triangular lattice Hubbard model: A dynamical cluster approximation study

2015 ◽  
Vol 91 (15) ◽  
Author(s):  
Hung T. Dang ◽  
Xiao Yan Xu ◽  
Kuang-Shing Chen ◽  
Zi Yang Meng ◽  
Stefan Wessel
Keyword(s):  
Hubbard Model ◽  
Triangular Lattice ◽  
Mott Transition ◽  
Cluster Approximation ◽  
Dynamical Cluster Approximation

scholarly journals Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

2000 ◽  
Vol 61 (19) ◽  
pp. 12739-12756 ◽  
Author(s):  
M. H. Hettler ◽  
M. Mukherjee ◽  
M. Jarrell ◽  
H. R. Krishnamurthy
Keyword(s):  
Electron Systems ◽  
Cluster Approximation ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Dynamical Cluster Approximation

Dynamical Cluster Approximation

2011 ◽  
pp. 271-302 ◽  
Author(s):  
H. Fotso ◽  
S. Yang ◽  
K. Chen ◽  
S. Pathak ◽  
J. Moreno ◽  
...  
Keyword(s):  
Cluster Approximation ◽  
Dynamical Cluster Approximation
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