Computational Studies of Correlated Electrons in One-Dimension
Sengupta, Pinaki
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https://hdl.handle.net/2142/31332
Description
Title
Computational Studies of Correlated Electrons in One-Dimension
Author(s)
Sengupta, Pinaki
Issue Date
2001
Doctoral Committee Chair(s)
Campbell, D.K.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
extended Hubbard model
Peierls-extended Hubbard model
electron-phonon coupling
Language
en
Abstract
"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one
dimension using primarily computational methods. We discuss the derivation of the models and
the computational methods used to study them, focusing primarily on our extensions over existing
numerical methods. In particular, we present the construction of ""operator-loop"" updates
for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series
Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve
the quality of the numerical data. For the extended Hubbard model at half-filling, we have
confirmed the existence of a recently reported bond-order wave phase for the ground state in a
small region of parameter space between the well-known charge- and spin-density wave phases.
We have studied in detail the nature of the associated quantum phase transitions between all
the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped
long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid
with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes
both electron-phonon and electron-electron interactions, we have studied the dimerization
transition of the half-filled system in the presence of fully quantum mechanical phonons. We
show that the transition to a dimerized state occurs only when the electron-phonon coupling
exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to
previous studies in similar models with adiabatic phonons that had predicted a dimerized state
for arbitrarily small values of the electron-phonon coupling."
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