Collective Phenomena In Strongly Correlated Frustrated Quantum Systems
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Date
2011-10-19
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[Bloomington, Ind.] : Indiana University
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Abstract
We study the role of lattice frustration, competing interactions and quantum
fluctuations in stabilizing non-trivial states of matter in strongly correlated
systems. Our analysis focuses on three types of physical phenomena: magnetism
in Mott insulators, superconductivity in repulsive fermion systems and
multiferroicity in complex oxides.
In the context of frustrated magnets, we propose a real-space mean-field
framework, which combines exact diagonalization in finite clusters and
variational calculation of the state of an infinite system, thus capturing
local correlations and providing a controlled and unbiased approximation
scheme. This method is applied to several models of quantum magnetism, such
as the square-lattice Heisenberg antiferromagnet with competing first and second
neighbor exchange interactions. Using a {it single} variational ansatz for the
ground state, we compute the zero-temperature phase diagram of this model,
which includes a quantum paramagnetic state. We show that this state has a
correlated plaquette nature and breaks translational invariance, but preserves
lattice point-group symmetries. Next, we study the phenomenon of magnetization
plateaux in the orthogonal dimer compound $scbo$, described by the
Shastry-Sutherland model. We demonstrate that plateaux are stabilized in
certain spin patterns, satisfying {it local} commensurability conditions,
which we also derive.
Lattice frustration usually hinders the existence of a long-range order.
However, in some cases frustration can be beneficial for stabilizing an ordered
state, even in a strongly interacting system. We illustrate this mechanism, by
considering the Hubbard model with modulated electron hoppings. Within a
controlled approximation, we demonstrate how magnetic fluctuations lead to a
$d$-wave superconducting state for {it arbitrarily} strong fermion repulsion.
We also discuss the possibility to observe this phenomenon in cold atom
experiments.
Another class of systems, where frustration and quantum fluctuations serve as
prerequisites for a complex ordered state, are multiferroics with
ferroelectricity due to charge ordering. Using the rare-earth oxide $lfo$ as
an example, we present a theory of multiferroic behavior, caused by the lattice
frustration and order-from-disorder physics. Using this theory we explicitly
demonstrate that the double exchange mechanism leads to a significant coupling
between electric and magnetic orders.
Description
Thesis (Ph.D.) - Indiana University, Physics, 2011
Keywords
quantum magnetism, frustration, order from disorder, superconductivity
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Doctoral Dissertation