Matrix Product States of Quantum Systems on Higher Dimensional Lattices
Project/Area Number |
24654042
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Global analysis
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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
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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Keywords | 量子スピン系 / 関数解析 / 基底状態 / エンタングルメント・エントロピー / 行列積状態 / PEP状態 / split property / entanglement entropy |
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.
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Report
(4 results)
Research Products
(6 results)