Collective Phenomena In Strongly Correlated Frustrated Quantum Systems

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.