Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit

Details Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit

2011-05-13

arxiv.org/abs/1105.2596v5

Physics

Condensed Matter

Statistical Mechanics

14 pages, 9 figures

Scientific paper

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 the 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 boundary effects 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.

Affiliated with

Also associated with

No associations

Rating

Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26651