Systems with competing orders are of great interest in condensed matter physics. When
two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states.
In the first part of the thesis, we study the
attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis.
The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments.
We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors.
In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems.
We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange.
For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’
states. For S=1/2, this lattice nematic takes the form of a valence bond solid.
With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO.
We discuss implications for the honeycomb lattice Hubbard model.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/32868 |
| Date | 31 August 2012 |
| Creators | Ramachandran, Ganesh |
| Contributors | Paramekanti, Arun |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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