Dr. Yu-Kun Huang
(黄玉坤 博士，Department of Electrical Engineering, Nan Jeon Institute of Technology, Tainan, Taiwan)
E-mail: ykln@mail.njtc.edu.tw
Abstract: We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the thermodynamic limit. The BMPS is built on a dual series of reduced biorthonormal bases for the left and right Perron states of a non-Hermitian matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG) algorithms and compare their numerical performance in both finite and infinite systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which are translationally invariant in the thermodynamic limit. We also develop an efficient wave function transformation of the iBTMRG, an analogy of McCulloch in infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as the lattice size is increased. The resulting iBMPS allows for probing bulk properties of the system in the thermodynamic limit without the boundary effect and allows for reducing the computational cost to be independent of the lattice size, which are illustrated by calculating the magnetization as a function of the temperature and the critical spin-spin correlation in the thermodynamic limit for a 2D classical Ising model.
Yu-Kun Huang received his BS degree in civil engineering and MS degree in applied mechanics from National Taiwan University, Taipei, Taiwan, in 1987 and 1989, respectively. Recently, He received his PhD degree in electrical engineering from National Chung Cheng University, Chiayi, Taiwan, in 2010. He is currently an Associate Professor in the Department of Electrical Engineering, Nan Jeon Institute of Technology, Tainan, Taiwan. His research interests span statistical mechanics, numerical methods in strongly correlated physics, and biomedical image analysis.
Location: 606 conference room
Date and time: July 25th, 2011 10:00 A.M.
