# Indiana University

 dc.contributor.advisor Ortiz, Gerardo en dc.contributor.author Isaev, Leonid en dc.date.accessioned 2011-10-19T20:18:13Z en dc.date.available 2028-06-19T20:18:13Z en dc.date.available 2012-02-19T00:56:24Z dc.date.issued 2011-10-19T20:18:13Z en dc.date.submitted 2011 en dc.identifier.uri http://hdl.handle.net/2022/13691 en dc.description Thesis (Ph.D.) - Indiana University, Physics, 2011 en dc.description.abstract We study the role of lattice frustration, competing interactions and quantum en 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. dc.language.iso en en dc.publisher [Bloomington, Ind.] : Indiana University en dc.rights Attribution 3.0 Unported en dc.rights.uri http://creativecommons.org/licenses/by/3.0/ en dc.subject quantum magnetism en dc.subject frustration en dc.subject order from disorder en dc.subject superconductivity en dc.subject.classification Condensed Matter Physics en dc.title Collective Phenomena In Strongly Correlated Frustrated Quantum Systems en dc.type Doctoral Dissertation en
﻿