Quantum antiferromagnets, fractional quantum Hall effect
The SU(N) antiferromagnet on a simple cubic lattice undergoes a phase transition from the Neel ordered phase to a disordered phase. The fluctuations in the Neel ordered phase are described by a nonlinear [sigma] model. The fluctuations in the disordered phase lead to a compact U(1) gauge theory, which goes through a phase transition. In the extreme quantum mechanical region (n[sub c] small), the ground state has broken translational symmetry and is in a spin-Peierls state. The degeneracies of the ground state are determined by n[sub c][identical to](mod 6). As one approaches the disorder-order phase transition line from below, one enters the RVB state. The Sp(M) generalization of the antiferromagnetic (AFM) Hamiltonian is used in studying the properties of the naturally frustrated triangular AFM. In the large M limit, the Sp(M) AFM undergoes a phase transition from ordered to disordered phase. The ordered phase has the classical 120[degrees] structure. It is concluded that the ground state of the S = 1/2 quantum AFM on a triangular lattice does have long-range order given by the classical 120[degrees] structure. At low temperatures, the system is described by an RVB state. By defining modular transformations for quantum Hall (QH) systems with fixed physical boundary conditions, it is shown that the lowest Landau level single particle and Laughlin's many-body wave functions form a basis for a reducible representation of the full modular group. The magnetic translation symmetry analysis of fractional QH systems with a periodic background gives a system-size dependent degeneracy for all the many-body eigenstates. A saddle point treatment of the Chern-Simons field theory gives the Hall conductance of a partially full subband to be a fraction. The statistics and the charge of the exotic quasiparticles and the ground state degeneracy in the thermodynamic limit are determined by the total Hall conductance of the system.
- Research Organization:
- Yale Univ., New Haven, CT (United States)
- OSTI ID:
- 7112209
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTIFERROMAGNETIC MATERIALS
HALL EFFECT
ORDER-DISORDER TRANSFORMATIONS
LATTICE FIELD THEORY
NEEL TEMPERATURE
SU GROUPS
FIELD THEORIES
LIE GROUPS
MAGNETIC MATERIALS
MATERIALS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
665400* - Quantum Physics Aspects of Condensed Matter- (1992-)
662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)