ELFT HÍRADÓ

[Janos Asboth <asboth.janos AT ttk.bme.hu>]

Meghívó

BME Elméleti Fizika Szeminárium,

máj. 26. péntek 10h15,

1111 Budapest, Budafoki út 8., BME F III. magasföldszint 01.,
Elméleti Fizika Tanszék szemináriumi szoba

Hetényi Balázs (BME Elm. Fiz. tanszék):
Extending the geometric phase formalism to cycles with isolated degeneracy
points and how to implement finite size scaling in the modern polarization
theory

The modern theory of polarization casts the dielectric polarization as a
geometric phase (Zak-Berry phase).   Due to the fact that this quantity is
not a simple operator expectation value, traditional finite size scaling
approaches are not applicable to it.  In systems where a local order
parameter exists, the Binder cumulant (a ratio of statistical cumulants) is
guaranteed to locate classical and quantum phase transition points via the
finite size scaling hypothesis.  In this talk, it will be shown that the
so-called gauge invariant cumulants associated with the geometric phase can
be used to construct the analog of the Binder cumulant for adiabatic
cycles.  The formalism is general, in the sense that such "Berry-Binder
cumulants" can be constructed for any adiabatic cycle with isolated
degeneracy points, and they take particular finite values at gap closure.
We apply the formalism to the location of gap closure points in a variety
of systems in one and two dimensions, including topological, disordered,
and correlated systems.  Our approach is sensitive to gap closure, even in
cases where the Fermi surface is down by two dimensions compared to the
dimension of the system (Dirac points in graphene or the topological
Haldane model).  We also develop a renormalization scheme based on the
modern polarization theory, and apply it to disordered systems in one, two,
and three dimensions.  In one and three dimensions our approach concurs
with the famous "gang-of-four" results, in two dimensions we run into
system size limitations, but our preliminary results are not inconsistent
with the scaling theory of localization.

[1]: B. Hetényi and B. Dóra, "Quantum phase transitions from analysis of
the polarization amplitude", Phys. Rev. B 99 085126 (2018).
[2]: B. Hetényi, "Interaction-driven polarization shift in the t-V-V'
lattice fermion model at half filling: emergent Haldane phase", Phys. Rev.
Research, 2 023266 (2020).
[3]: B. Hetényi, S. Parlak, and M. Yahyavi, "Scaling and renormalization in
the modern theory of polarization: application to disordered systems",
Phys. Rev. B 104 214207 (2021).
[4]: B. Hetényi and S. Cengiz, "Geometric cumulants associated with
adiabatic cycles crossing degeneracy points: Application to finite size
scaling of metal-insulator transitions in crystalline electronic systems"
106 195151 (2022).

Minden érdeklődőt szeretettel várunk.
Asbóth János,
 szemináriumi koordinátor

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