Matrix Product States of Quantum Systems on Higher Dimensional Lattices

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654042
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: MATSUI Taku 九州大学, 数理(科)学研究科(研究院), 教授 (50199733)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 量子スピン系 / 関数解析 / 基底状態

Outline of Final Research Achievements

(i) We considered 2dim (infinite) quantum spin systems and obtain PEPS representations for any translationally invariant states using using representations of a quadruplet of Cuntz algebras. Our construction is a generalization of the correspondence of Cuntz algebras and matrix product states in 1 dim quantum systems.(ii) We obtained a class of formal Hamiltonians for Bosonic systems on lattices for which frustration free ground states exist.

Free Research Field

数理物理