2019 Fiscal Year Research-status Report
Critical properties of quantum melting phase transitions
| Project/Area Number |
18K13502
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| Research Institution | Keio University |
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Principal Investigator |
BEEKMAN ARON 慶應義塾大学, 自然科学研究教育センター(日吉), 訪問研究員 (90632985)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | quantum phase transition / quantum melting / liquid crystals / renormalization group / particle-vortex duality |
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| Outline of Annual Research Achievements |
The functional renormalization group (FRG) study reported in FY2018 was amended and published in FY2019. This was a prerequisite, simplified case of the full model under investigation. In FY2019 we aimed to make this extension, and preliminary investigations (implementing the crystal dynamics in the dual gauge fields and the so-called glide constraint in the dual dislocation condensate) were undertaken. FRG calculations are started with Dr. Fejos, while new insights from "fractons" into the glide constraint are studied with Dr. Nissinen.
On the other hand, several interesting related results have been obtained. The quantum melting phase transition relies entirely on the concept of spontaneous symmetry breaking, on which we have published a comprehensive review/tutorial. A generalization of the Josephson effect to among others crystalline solids has been established, which also leads to a new observable for quantum liquid-crystalline order, at least in principle. Furthermore the previous FRG work led us to hypothesize that there may be a so-called charged fixed point also in exactly two dimensions, as a counterpoint to the BKT phase transition, or two-dimensional Abelian-Higgs model. This is work-in-progress with Dr. Fejos.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
Due to both technical complications related to FRG and the need to adapt to what has been recently uncovered in fracton physics, the calculations on the full model have not yet been completed. Furthermore, as the analytical framework is yet to be fully understood, the numerical calculations are also delayed.
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| Strategy for Future Research Activity |
The main focus is the analytical work, with its recently encountered complications, which we strive to complete in FY2020. Additional delay may result from the present problems in society, in particular the restriction on both international travel. The spin-off project on the charged fixed point in two dimensions partly overlaps with the extension to the full model and is expected to be completed simultaneously.
If time and external factors allow, implementation of the numerical calculations may still be undertaken in this year.
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| Causes of Carryover |
Expenditure was limited due to little international travel expenses, as well as no purchase of workstations for numerical work. It is probable no international conferences will take place current fiscal year, which will lead to equal expenditure savings. The research budget will be used for international collaboration, presentation at conferences if possible, and purchase or lease of numerical computer power if applicable.
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