Virtual Mathematics Colloquium -- Excitations, Spin-Charge Separation, and Correlation Function
This event is in the past.
2 p.m. to 3 p.m.
Speaker: Hai-Qing Lin (School of Physics, Zhejiang University)
Quasi-particles play important role in condensed matter physics and result in many emergent novel phenomena. In this talk, we discuss collective excitations in one-dimension as exemplified by antiferromagnetic Heisenberg model and δ-function interacting Fermi gas (Yang-Gaudin model). Using the thermodynamic Bethe Ansatz (TBA) formalism, we analytically derive universal properties of the models with arbitrary interaction strength, and present a rigorous understanding of spin-charge separation, a unique feature predicted by the Tomonaga-Luttinger liquid (TLL) theory. Spinon, as an elementary spin excitation, is responsible for the TLL. We show that a dimensionless quantity, the Wilson Ratio (WR), elegantly characterizes quantum liquid phase diagram. For the TLL phase, WR = 4Ks remains almost temperature independent, where Ks is the Luttinger parameter. WR can be used to identify quantum phase transitions for a wide variety of materials. Based on the exact low-lying excitation spectra, we further evaluate the spin and charge dynamical structure factors (DSFs). The peaks of the DSFs exhibit distinguishable propagating velocities of spin and charge as functions of interaction strength, which can be observed by Bragg spectroscopy with ultracold atoms. Combining quantum integrable theory with numerics, we propose a reliable technique to exactly compute the spectral function of 1D many-body models at large scales and demonstrate the technique on the Lieb-Liniger gas. Our results show that a full description of the critical behavior requires system size as large as thousands of particles.
Event changed to virtual due to weather!
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Meeting ID: 973 5469 2476
Guan XW Group: Feng He, Yu-Zhu Jiang, Yi-Cong Yu, Yang-Yang Chen
CSRC & Other Institutes: Song Cheng, Rubem Mondaini, Wen-Li Yang
Rich Univ./US: Randall G. Hulet, Han Pu
Univ. of Warwick/UK: Rudolf A. Romer
Bethe Ansatz Group: X.-G. Yin A. Foerster, M. T. Batchelor, C.-H. Lee