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Field theoretical methods for strongly correlated electron systems

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Title: Field theoretical methods for strongly correlated electron systems
Author(s): Cassanello, Carlos Raul
Doctoral Committee Chair(s): Fradkin, E. H.
Department / Program: Physics
Discipline: Physics
Degree: Ph.D.
Genre: Dissertation
Subject(s): electron systems field theory (physics) large n-slave fermion Quantum Physics Condensed Matter Physics
Abstract: Large N - slave fermion techniques have been established as a powerful computational tool to study quantum many-body systems. They have been applied successfully to the study of various systems of strongly correlated electrons in condensed matter physics, particularly to problems where a non-perturbative treatment is required. In the first part of this thesis we use this approach to investigate the Frustrated Quantum Antiferromagnet. We study the Chiral Spin Liquid state of the antiferromagnet at zerotemperature, which has a spin-gap generated by the spontaneous breakdown of time-reversalsymmetry. This state is known as the Chiral Spin State. We determine conditions for the restoration of time-reversal-symmetry in a bilayer antiferromagnet with an interlayer exchange interaction. We show the energetically favored ground state has Chiral Spin Liquids with opposite chiralities on each layer. This constitutes a dynamic mechanism which prevents the observation of broken time-reversal-symmetry in a bilayer system, even though this breakdown may be present on each layer independently. In the second part of this thesis we use the slave-fermion technique to study the physics of magnetic impurities both in Quantum Antiferromagnets (in a flux phase) and in d-wave superconductors. This is a system consisting of a magnetic impurity coupled to either the low lying excitations of a flux phase, or to the normal quasi-particles close to the Fermi surface of a superconductor whose gap function exhibits nodes. We show that both systems display a zero temperature quantum phase transition in the large N approximation. The transition takes place between a weak coupling regime, in which the magnetic impurity is effectively decoupled from the quasi-particles, to a strong coupling phase which exhibits a Ill Kondo effect and the magnetic impurities are screened. The ground state is a singlet. If the system has particle-hole symmetry the impurity appears to be overscreened. This effect is not due to a multichannel character in the system. The physical origin of the quantum phase transition is directly related to the fact that this is a non-marginal Kondo system. This follows from having a quasi-particle band with a density of states that vanishes linearly with the energy in the proximity of the Fermi surface. We show that, due to the presence of nodes in the gap function of a d-wave superconductor, there is a striking analogy between the problem of a Kondo impurity coupled to a flux phase and a magnetic impurity coupled to the superconductor. We consider a clean dx2-y2 superconductor in the presence of a fully quantum mechanical magnetic impurity. It is assumed that the temperature is sufficiently low so as to neglect both phase and amplitude fluctuations of the order parameter. We study the zero temperature behavior and the low temperature and low magnetic field regimes in the vicinity of the quantum phase transition. In the strong coupling phase, we obtain scaling behavior for the chemical potential of the impurity f.J and for the amplitude of the ground state singlet ~- At zero temperature we show that they present different scaling behavior with the distance to critical coupling: EJ scales linearly while ~ scales with a vanishing exponent. Both magnitudes present logarithmic corrections to scaling suggesting that the theory may be at an upper critical dimension. At finite field (zero temperature) and/or at finite temperature (zero field), at the critical coupling the magnetic field or the temperature respectively, play a similar role as the distance to the critical coupling in the scaling formulas. The susceptibility and the specific heat are investigated both at zero temperature, zero field limit and at low temperature, low field regimes. The results are consistent with the existence of perfect screening and a singlet ground state in the strong coupling phase. When particle-hole is an exact symmetry of the system, the impurity appears to be overscreened with a vanishing paramagnetic susceptibility.
Issue Date: 1996
Genre: Dissertation / Thesis
Type: Text
Language: English
URI: http://hdl.handle.net/2142/18856
Rights Information: 1996 Carlos Raul Cassanello
Date Available in IDEALS: 2011-04-21
Identifier in Online Catalog: 4011027
 

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