One dimensional antiferromagnetic spin systems.
Item
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Title
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One dimensional antiferromagnetic spin systems.
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Identifier
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AAI3024840
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identifier
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3024840
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Creator
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Sun, Ping.
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Contributor
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Adviser: David Schmeltzer
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Date
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2001
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Condensed Matter | Physics, Electricity and Magnetism
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Abstract
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In the thesis, I discuss various physical properties of the one dimensional antiferromagnetic spin-1/2 systems by using mainly analytical tools of bosonization and renormalization group. I describe in details the bosonization method using the functional integral formalism based on the work of D. Schmeltzer. I present a continuous differential renormalization group approach which works in the hamiltonian formalism. I apply these tools to study the spin systems. I first show how this works on a single spin chain. I compare the result of the spin liquid fixed points from our approach with that from the Bethe ansatz and find excellent coincidence. I then study the problem of a single spin chain in a weak external magnetic field. I find that, due to the field, the spin system flows to a different fixed point. The deviation shows a weak singular behavior which appears in measurable quantities like the spin susceptibility. The spin-spin correlations and susceptibilities are calculated. The next subject is on the spin-Peierls system. I show an SU(2) symmetry relation via chiral fermion representation among the three possible phases, the spin liquid phase, the antiferromagnetically ordered phase, and the valence bond solid phase. We use the two cutoff renormalization group method and find reliable phase diagrams in various circumstances. Our approach is a unified method which works in both the high and low frequency regions. The last topic I discuss is the coupled spin chains. By carefully keeping the full hamiltonian instead of starting with the spin model at the Heisenberg fixed point, I discuss the two leg and three leg ladders and show the former is gapped while the later gapless. In the case of the two leg ladder, a different asymptotic behavior in the weak inter-chain coupling limit is found.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
