2020 Fiscal Year Annual Research 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 / symmetry breaking / renormalization group |
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| Outline of Annual Research Achievements |
In the final year of the project, we attempted to resolve the functional renormalization-group issues plaguing the main problem as well as the spin-off problem on two-dimensional charged fixed points. Unforeseeable beforehand, the technical problems involved in these calculations were of such large extent that completion of the project was not possible in this time frame. The crucial issue is the wavefunction renormalization of the scalar field in combination with that of the gauge field in the so-called R_xi gauge fixes. It is now expected that other methods might be more applicable. We have nevertheless uncovered several insights and pointers for future research in the quantum melting phase transition of solids to quantum liquid crystals, both theoretical and experimental, that will be outlined in the final report.
An investigation on the generalization of the Josephson effects from superconductivity to any ordered state of matter was completed. Such effects could in principle also be used to detect the presence of quantum-crystalline phases of matter. Furthermore part of the research will be featured in an upcoming textbook "Spontaneous Symmetry Breaking" to be published by Cambridge University Press.
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