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For my dissertation at the University of Maryland, and as a post-doctoral
fellow at Penn State, I studied many electron problems where the
correlation effects are
such that they have to be treated in a careful manner beyond the standard
perturbative treatments of electron correlations. These problems I
have addressed using Quantum Monte Carlo(QMC)
methods.
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Hubbard model and high-temperature superconductivity
Electron correlation effects are well studied in a lattice model, known as
Hubbard Model where correlation are introduced through (i})
the constraints
that no two electrons with the same spin can occupy the same lattice site
and ( ii) an additional cost in energy if two electrons with different
spins occupy the same site. Following the discovery of
high temperature
supercondictivity(HTSC) a general belief grew that
high transition temperature can only result from electron-electron
(and not electron-phonon) interactions. Many new ideas were introduced using
Hubbard model as the paradigm of these theories.
I have studied some aspects of HTSC both in simple and a multi-band
Hubbard Model by use of QMC methods which have become very powerful tools
to take into account strong electron correlations properly
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Aniket Bhattacharya and C. S. Wang
The generalized flux phases, Hubbard versus t-J model
Rapid Communication, Phys. Rev. B, 45 , 10826 (1992).
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Aniket Bhattacharya and C. S. Wang
Spin and charge fluctuations in an extended Hubbard
model of oxide superconductors
Phys. Rev. B, 48, 13949 (1993).
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Exact Green's function Quantum Monte Carlo methods applied
to small clusters
At Penn State, I worked on calculating ground states energies of small
clusters which are very weakly bound. For example the binding energy
for the dimer He-H is of the order of 8kT only.
It is difficult to
extract such a small number accurately. So we used an exact
Quantum Monte Carlo method which is computationally feasible
for only small number of electron. The important fact is that
these calculations are exact in the sense that
it requires no further approximations beyond what is involved in
Schrodinger equation; the only error involved is that of statistical
sampling error.
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Aniket Bhattacharya and J. B. Anderson
An exact quantum Monte Carlo calculation of the H-He interaction
potential
Phys. Rev. A, 49, 2441 (1994).
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Aniket Bhattacharya and J. B. Anderson
Interaction potential of a symmetric helium trimer
J. Chem. Phys, 100, 8999 (1994).
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