期刊
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
卷 -, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/aa9dcb
关键词
entanglement entropies; quantum phase transitions; spin chains; ladders and planes; rigorous results in statistical mechanics
资金
- [IBS-R018-D2]
- Ministry of Science & ICT (MSIT), Republic of Korea [IBS-R024-D1-2018-A00] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
Area law violations for entanglement entropy in the form of a square root has recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by elements of a {\it Symmetric Inverse Semigroup} with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, S-1(3), S-2(3), and S-1(2),The system based on S-1(3) and S-2(3) provide examples of quantum phase transitions in one dimensions with the former exhibiting a transition between the area law and a logarithmic violation of the area law and the latter providing an example of transition from logarithmic scaling to a square root scaling in the system size, mimicking a colored S-1(3) system. The system with S-1(2) is much simpler and produces states that continue to obey the area law.
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