ABSTRACT
Quasiparticles play an important role in condensed matter physics and result in many emergent novel phenomena. In this talk, we discuss collective excitations in one dimension, exemplified by the 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 the 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. We further evaluate the spin and charge dynamical structure factors (DSFs) based on the exact low-lying excitation spectra. 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 a system size as large as thousands of particles.
BIOGRAPHY
Prof. Hai-Qing Lin received his BS from The University of Science and Technology of China in 1981 and his PhD in physics from University of California, San Diego in 1987. He spent a few years as Research Associate in Brookhaven National Lab and Los Alamos Nationa lab, and joined University of Illinios at Urbana Champaign as Research Assistant Professor in 1991. He then joined the Chinese University of Hong Kong as a Professor in 1995 and worked for 17 years there as a Professor. He moved to Beijing Computational Science Research Center (CAEP) in 2009 and then assumed his most recent position as a Professor at School of Physics, Zhejiang University, in January 2022. Prof. Lin's research expertise is in condensed matter physics and computational physics. His main research interests include the physics of strongly correlated systems, quantum phase transition, quantum entanglement, and numerical methods for many-body systems.
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