Renormalization Group Theory and Sine-Gordon Model Lectures
Explore the concepts of Renormalization Group Theory and the Sine-Gordon Model in these insightful lectures, covering topics such as the Kosterlitz-Thouless Phase Diagram, Spin Lattices, and Critical Scales. Gain a deeper understanding of phase transitions and gap behaviors within the strong coupling regime.
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Renormalization Group Theory & Sine-Gordon Model Mariana Malard
Renormalization Group Theory & Sine-Gordon Model SUMMARY OF THE LECTURES Lecture 4 January 28th Finish from last lecture: Kosterlitz-Thouless Phase Diagram Gap
Spin Lattices, Spin Waves, Non-linear Sigma Model SUMMARY OF THE LECTURES Lecture 5 January 30th Conceptual overview. Spin-wave theory. Break-down of spin-wave theory for D = 1 antiferromagnets. Mapping onto the non-linear sigma model (time permitting).
Kosterlitz-Thouless Phase Diagram At this critical scale, interactions become too strong, i.e. strong enough to win over the kinetic term in H. Past this scale, R.G. is no longer valid. System undergoes a phase transition from gapless to gapped bosons. Bosons become trapped at the cosine minima. u xlc 1 . . . . . . . . . .. . . . .. . . . . K 0 1 The critical correlation length decreases as one goes deeper inside the strong coupling regime.
Kosterlitz-Thouless Phase Diagram Gap long (short) critical scale small (large) gap What is the value of lc ? Flow equations up to first order in u:
Kosterlitz-Thouless Phase Diagram Gap First-order flow diagram: ? ? = ?0
Kosterlitz-Thouless Phase Diagram Gap Critical scale: ?0 < 1 and ?0 1 with 1st order gap:
Kosterlitz-Thouless Phase Diagram Gap The critical correlation length decreases, as thus the gap becomes larger, as one goes deeper inside the strong coupling regime.
Kosterlitz-Thouless Phase Diagram Gap gapped gapless Phase transition
Kosterlitz-Thouless Phase Diagram Gap Approximation to 2nd order gap: gapped gapless 1
Kosterlitz-Thouless Phase Diagram Homework Find some experimental papers on realizations of Kosterlitz-Thouless phase transitions in one- dimensional interacting electron systems, both for the charge sector (Umklapp scattering needed) and for the spin sector (backscattering needed).
