Tensor network study of non-magnetic phases in quantum spin systems

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400392
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kyoto University
• Principal Investigator: Harada Kenji 京都大学, 情報学研究科, 助教 (80303882)
• Research Collaborator: MORITA Satoshi 東京大学, 物性研究所, 助教
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: テンソルネットワーク / 脱閉じ込め量子臨界現象 / SU(N)対称性 / 反強磁性ハイゼンベルグモデル / valence-bond solid state

Outline of Final Research Achievements

We numerically study thermal phase transitions of generalized SU(N) Heisenberg models on square and honeycomb lattices. They are critical near zero temperature, and the universality classes on square and honeycomb lattices are the weak Ising one and the three-state Potts one, respectively. For the scaling analysis of critical phenomena, we propose a new Bayesian scaling analysis with corrections to scaling. We show the fast convergence of the value of inverse temperature and critical indexes by our new method for the thermal phase transition of the three-dimensional Ising model. We also numerically study the ground state phase diagram of SU(N) Heisenberg models with multi-column representations on square lattices. We estimate the minimum system size to check the existence of very weak dimer order for three-column representations. For large-scale tensor network calculation, we develop a parallel tensor network library based on the standard parallel linear-algebra library.

Free Research Field

物性基礎論