The key to understanding interacting many-body systems at low temperatures is often to identify their dominant ordering pattern. Though some types of order seem extremely robust and prevalent in nature, those which lie at the frontier of our understanding are often the result of subtle competition between interactions, and hence can be delicate and difficult to identify. This competition can lead to intricate phase diagrams, as varying parameters favors different orders. They often also exhibit surprising emergent properties, including deconfined gauge fields or topological order not present in the microscopic model. Understanding the nature and scope of these novel orders is one of the key tools in mastering the vast practical and intellectual potential of low-temperature correlated materials.
In this thesis, we explore intricate orders, both classical and quantum, which emerge in several strongly correlated systems at low temperature. In Chapter 2, we investigate magnetic ordering in classical antiferromagnets on a class of dilutions of the face-centered cubic lattice. Exploiting the fact that the magnetic Hamiltonian is that of a particular stacking of triangular planes, we find a 120 degree order for Heisenberg and XY magnets, and an entropically driven 3-sublattice order in the Ising case. In Chapter 3, we propose a (topologically ordered) gapless spin liquid state in the highly frustrated pyrochlore antiferromagnet. We find the energetically favored symmetric spin liquid state using a large Nf expansion, and present arguments for its stability to fluctuations about the infinite Nf mean-field state. Chapter 4 explains and generalizes an interesting relationship between the algebraic structure of these states and the representation theory of Lie groups. Chapter 5 turns to a classical ordering with a fractal, devil’s staircase structure found in 1-d systems with infiniteranged interactions. The fate of these states in dipolar bosonic gases, where quantum effects come into play, is investigated—along with an interesting generalization of the classical problem. Finally, in Chapter 6 we consider how to stabilize states exhibiting the topological order of fractional quantum Hall states in 3 dimensional crystals, finding a parameter regime in doped graphite in which such states appear energetically favorable.
|Advisor:||Sondhi, Shiraji L.|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 70/10, Dissertation Abstracts International|
|Subjects:||Condensed matter physics, Theoretical physics|
|Keywords:||Correlated systems, Magnetic ordering, Quantum Hall|
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