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SUMMARY:Direct detection of metal-insulator phase transitions using modifi
ed Backus-Gilbert method
DTSTART;VALUE=DATE-TIME:20170623T132000Z
DTEND;VALUE=DATE-TIME:20170623T134000Z
DTSTAMP;VALUE=DATE-TIME:20200219T032152Z
UID:indico-contribution-282@cern.ch
DESCRIPTION:Speakers: Dr. ULYBYSHEV\, Maksim (University of Regensburg)\nT
he detection of the (semi)metal-insulator phase transition can be extremel
y difficult if the local order parameter which characterizes the ordered p
hase is unknown. In some cases\, it is even impossible to define a local o
rder parameter: the most prominent example of such system is the spin liqu
id state. This state was proposed to exist in the Hubbard model on the hex
agonal lattice in a region between the semimetallic phase and the antiferr
omagnetic insulator phase. The existence of this phase has been the subjec
t of long debates.\n\nAnother example with similar difficulties is graphen
e in magnetic field: it is definitely in the insulating state\, which is c
onfirmed by experiments\, but the type of ordering is unknown. There are s
everal types of local order that have been proposed so far. Some of them
(for instance\, the Charge Density Wave) are even impossible to detect in
a usual way where the small mass term is added as a seed for the phase tr
ansition and the corresponding susceptibility is calculated in the limit o
f zero mass. The problem with this approach appears because the mass term
for the Charge Density wave produces a sign problem.\n\nThus\, some alter
native methods for the detection of the phase transitions in such cases sh
ould be developed. We modified the Backus-Gilbert method of analytical co
ntinuation which was previously used in the calculation of the pion quasip
article mass in lattice QCD. The modification of the method consists of th
e introduction of the Tikhonov regularization scheme which was used to tre
at the ill-conditioned kernel.\nFurthermore\, in some cases\, additional a
veraging over judiciously chosen intervals in Euclidean time was introduce
d in order to suppress statistical fluctuations in the input data. \n\nThi
s modified Backus-Gilbert method is applied to the Euclidean propagators i
n momentum space calculated using the Hybrid Monte Carlo algorithm. In thi
s way\, it's possible to reconstruct the full dispersion relation and to e
stimate the mass gap\, which is the direct signal of the transition to the
insulating state. We demonstrate the ability of the method in the calcu
lations for the Hubbard model on the hexagonal lattice and for graphene in
a magnetic field. We also apply the method to the metal-insulator phase t
ransition in the Hubbard and Hubbard-Coulomb models on the square lattice.
The access to the full dispersion relation gives us a possibility to chec
k the appearance of the momentum-dependent mass gap ("pseudogap" state) a
nd it's dependence on the details of electron-electron interaction.\n\nhtt
ps://makondo.ugr.es/event/0/session/101/contribution/282
LOCATION: Seminarios 1+2
URL:https://makondo.ugr.es/event/0/session/101/contribution/282
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