In this talk I will present some recent progress on the construction of ground state of the honeycomb Hubbard model, which is a prototypical model for studying phase transitions in quantum many-body system. Using fermionic cluster expansions and constructive renormalization theory, we proved that the ground state of this model is not a Fermi liquid in the mathematical precise sense of Salmhofer. We also derived the non-perturbative critical temperature for the phase transition. This presentation is based on the joint work with V. Rivasseau: arXiv:2108.10852.
Zhituo Wang is an associate professor at the institute of advanced study in mathematics (IASM), Harbin Institute of Technology. He obtained a Ph.D in 2011 at the University of Paris-sud 11. His supervisor was Prof. V. Rivasseau. Then he became a posdoc researcher at the university of Roma Tre. His mentors were V. Mastropietro and A. Giuliani. His current interest is constructive quantum field theory, quantum many-body problem, probability and noncommutative geometry.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai