| 研究課題/領域番号 |
18K13502
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| 研究機関 | 慶應義塾大学 |
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研究代表者 |
BEEKMAN ARON 慶應義塾大学, 理工学部(矢上), 特任助教(非常勤) (90632985)
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| 研究期間 (年度) |
2018-04-01 – 2021-03-31
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| キーワード | quantum phase transition / quantum melting / liquid crystals / renormalization group / particle-vortex duality |
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| 研究実績の概要 |
As a fortuitous circumstance, Dr. Gergely Fejos happened to join our department this fiscal year. He is an expert on the Functional Renormalization Group (FRG) method and has determined the critical structure of the one-field gauge model before. We decided to apply this method as well to the present problem of the two-field gauge model, instead of the originally proposed field-theoretic renormalization group calculation. We believe FRG is superior because flow equations are evaluated at a single energy scale as opposed to two separate energy scale, and because the dimension-dependent behaviour can be readily studied.
In FY2018 we completed the FRG study of a simplified model with two order parameter fields and two gauge fields. The results, interesting of itself from a renormalization-group point of view, indicate that the solid-to-hexatic quantum phase transition where both order parameter fields condense at the same time, is viable and would be of the expected second-order kind. However, in this simplified model the critical point lies in the U(1) universality class, which would make it difficult to experimentally distinguish from other possible phase transitions. It is to be seen whether the universality class is actually different for the full model. This is the topic of current work.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
Due to collaboration with Dr. Fejos, the renormalization group calculation is completed ahead of the initial schedule, although it needs yet to be extended to the full model. While Dr. Nissinen has visited us to discuss the originally planned and presently undertaken work, we now believe the present program is the most promising.
On the other hand, due to focus on this analytic calculations, efforts on numerical works have been limited.
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| 今後の研究の推進方策 |
The direction is clear: the calculation on the simplified model needs to be extended to the full model. This consists of two complications: the gauge-field sector has more complex dynamics and the order-parameter sector needs to be supplemented with the so-called glide constraint, which protects the longitudinal sound mode that must indeed survive the dual condensation process. It is not yet clear whether these additions will modify the universality class of the critical point, and this is the most pressing issue experimentally. We aim to complete this calculation in FY2019, if no unforeseen obstruction arise.
The next step is to use the result of that calculation to obtain the properties of the critical point, in particular critical exponents, which are the quantities to compare to experiment. This is expected for FY2019-2020.
Concurrently, the start-up of physical modelling and writing code for numerical calculations is planned for FY2019.
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| 次年度使用額が生じた理由 |
Because of the slight delay in the preparation for numerical calculations, no computer hardware has been purchased this year. When numerical modelling has commenced in FY2019, we will consolidate the carry-over budget with the FY2019 budget in order to acquire the hardware necessary to carry out the numerical calculations.
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