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[CM ICTP - Trieste]

SEMINAR on   Disorder and strong electron correlations


Tuesday, 9 October   -    12:30 hrs.



Seminar Room,  Main Bldg.- first floor


G. VOLOVIK   ( Helsinki University of Technology )

"Gap nodes protected by topology in momentum space and quantum phase 
transitions"

Abstract

	Many quantum condensed matter systems are strongly correlated and 
strongly interacting fermionic systems, which cannot be treated 
perturbatively.   However, physics which emerges in the low-energy 
corner does not depend on the complicated details of the system and is 
relatively simple. It is determined by the nodes in the fermionic 
spectrum, which are protected by topology in momentum space (in some 
cases, in combination with the vacuum symmetry).  Close to the nodes 
the behavior of the system becomes universal; and the universality 
classes are determined by the toplogical invariants in momentum space.  
When one changes the parameters of the system, the transitions are 
expected to occur between the vacua with the same symmetry but which 
belong to different universality classes.  Different types of quantum 
phase transitions governed by topology in momentum space are discussed. 
  They involve Fermi surfaces, Fermi points, Fermi lines, and also the 
topological transitions between the fully gapped states which 
experience intrinsic quantum Hall and spin Hall effects, etc.  The 
consideration based on the  momentum space topology of the Green's 
function is general and is applicable also to the vacua of relativistic 
quantum fields.  This is illustrated by the possible quantum phase 
transitions governed by topology of nodes in the spectrum of elementary 
particles of Standard Model.