非等方かつ長距離相関のある物理系に対する汎関数繰り込み群による理論的解析

• Project/Area Number: 13J06615
• Research Category: Grant-in-Aid for JSPS Fellows
• Allocation Type: Single-year Grants
• Section: 国内
• Research Field: 素粒子・原子核・宇宙線・宇宙物理(理論)
• Research Institution: The University of Tokyo
• Principal Investigator: 谷崎 佑弥 東京大学, 理学系研究科, 特別研究員(DC1)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,600,000 (Direct Cost: ¥3,600,000); Fiscal Year 2015: ¥1,200,000 (Direct Cost: ¥1,200,000); Fiscal Year 2014: ¥1,200,000 (Direct Cost: ¥1,200,000); Fiscal Year 2013: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: Lefschetz thimble / 符号問題 / 強結合フェルミオン系 / 汎関数繰り込み群 / フェルミオン多体系 / 超流動 / クロスオーバー

Outline of Annual Research Achievements

中性子性の中心付近では、非常に密度の高く冷たい核物質が存在すると考えられている。その極限的な状況下でどのような物性が発現するかを見るためには、核物質を記述する基本理論である量子色力学の立場から考えることは重要である。本年度の研究では、その際に障害となる有限密度量子色力学(QCD)の符号問題 を近年発達してきているLefschetz thimble上の経路積分に基づいて考察した。
本研究手法の基本的なアイディアは、多変数振動積分を評価する際に元の積分路を複素空間内で符号問題が緩和されるように変形させることである。Cauchyの積分定理のおかげでこの変形のもとで分配関数は変化せず、さらにPicard-Lefschetz理論により元の振動積分が収束性の良い積分の和に分解できる。この分解における各積分路はLefschetz thimbleと呼ばるので、この計算手法はLefschetz thimble上の経路積分と呼ばれている。
本年度は特に、軽いクォークを含むQCDの計算に現れる符号問題の構造について研究を行った。クォーク化学ポテンシャルμを導入すると、核子質量をMとしてμ<M/3でバリオン数密度が立ち上がるべきであると期待されているが、実際に有限密度QCDを近似的に計算するとパイオン質量の半分ですでにバリオン数密度が立ち上がってしまう。この非物理的な振る舞いを理解することが重要である。そこで問題を簡単化し、1サイトの電子系をLefschetz thimble上の経路積分を考察した。この模型は厳密に計算でき、さらにその符号問題の性質は有限密度QCDのそれと酷似している。そこでは、元の積分路が複数のLefschetz thimbleに分解され、それらを足し上げるときに起こる複素位相の干渉がこの現象の理解に重要であることを示した。この知見を実際のQCDに応用することは今後の課題である。

Research Progress Status

27年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

27年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] University of Illinois at Chicago/North Carolina State University/Harvard University(米国)
• [Int'l Joint Research] Heidelberg University/Bielefeld University(Germany)
• [Journal Article] Lefschetz-thimble analysis of the sign problem in one-site fermion model (2016)
  • Author(s): Yuya Tanizaki, Yoshimasa Hidaka, Tomoya Hayata
  • Journal Title: New Journal of Physics Volume: 18 Issue: 3 Pages: 1-14
  • DOI: 10.1088/1367-2630/18/3/033002
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method (2015)
  • Author(s): Kenji Fukushima, Yuya Tanizaki
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 111 Issue: 11 Pages: 1-11
  • DOI: 10.1093/ptep/ptv152
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] From quantum to classical dynamics: The relativistic O(N) model in the framework of the real-time functional renormalization group (2015)
  • Author(s): David Mesterhazy, Jan H. Stockemer, Yuya Tanizaki
  • Journal Title: Physical Review D Volume: 92 Issue: 7 Pages: 1-32
  • DOI: 10.1103/physrevd.92.076001
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral (2015)
  • Author(s): Yuya Tanizaki, Hiromichi Nishimura, Kouji Kashiwa
  • Journal Title: Physical Review D Volume: 91 Issue: 10 Pages: 1-6
  • DOI: 10.1103/physrevd.91.101701
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Lefschetz-thimble techniques for the path integral of zero-dimensional O(n) sigma models (2015)
  • Author(s): Yuya Tanizaki
  • Journal Title: Physical Review D Volume: 91 Issue: 3
  • DOI: 10.1103/physrevd.91.036002
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Structure of Lefschetz thimbles in simple fermionic systems (2015)
  • Author(s): Takuya Kanazawa, Yuya Tanizaki
  • Journal Title: Journal of High Energy Physics Volume: 1503 Issue: 3 Pages: 044-044
  • DOI: 10.1007/jhep03(2015)044
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Functional renormalization group approach to conventional theory of superfluidity and beyond (2014)
  • Author(s): Yuya Tanizaki, Gergely Fejos, Tetsuo Hatsuda
  • Journal Title: Journal of Physics: Conference Series Volume: 529 Pages: 012027-012027
  • DOI: 10.1088/1742-6596/529/1/012027
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Phase structure of SU(3) gauge-Higgs unification models at finite temperature (2014)
  • Author(s): Kouji Kashiwa, Yuya Tanizaki
  • Journal Title: Physical Review D Volume: 89 Issue: 11
  • DOI: 10.1103/physrevd.89.116013
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Many-body composite bosons from the viewpoint of functional renormalization (2014)
  • Author(s): Yuya Tanizaki
  • Journal Title: Bulgarian Journal of Physics Volume: 41 Pages: 180-186
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Real-time Feynman path integral with Picard-Lefschetz theory and its applications to quantum tunneling (2014)
  • Author(s): Yuya Tanizaki, Takayuki Koike
  • Journal Title: Annals of Physics Volume: 351 Pages: 250-274
  • DOI: 10.1016/j.aop.2014.09.003
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition (2014)
  • Author(s): Yuya Tanizaki, Gergely Fejos, Tetsuo Hatsuda
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2014 Issue: 4 Pages: 1-19
  • DOI: 10.1093/ptep/ptu035
  • Peer Reviewed
• [Journal Article] Functiona1 renormalization group approach to conventional theory of superfluidity and beyond (2014)
  • Author(s): Yuya Tanizaki, Gergely Fejos, Tetsuo Hatsuda
  • Journal Title: Journal of Physics : Conference Series Volume: (印刷中)
  • Peer Reviewed
• [Journal Article] Fermionic Functional Renormalization Group Approach to Bose-Einstein Condensation of Dimers (2014)
  • Author(s): Yuya Tanizaki
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2014 Issue: 2 Pages: 1-11
  • DOI: 10.1093/ptep/ptu009
  • Peer Reviewed
• [Journal Article] Flow equation of functional renormalization group for three-body scattering problem (2013)
  • Author(s): Yuya Tanizaki
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2013 Pages: 1-12
  • Peer Reviewed
• [Presentation] Lefshcetz-thimble path integral for studying the Silver Blaze phenomenon (2016)
  • Author(s): Yuya Tanizaki, Yoshimasa Hidaka, Tomoya Hayata
  • Organizer: 日本物理学会
  • Place of Presentation: 東北学院大学(宮城県仙台)
  • Year and Date: 2016-03-19
• [Presentation] Lefschetz-thimble and complex Langevin approaches to Silver Blaze of one-site Hubbard model (2015)
  • Author(s): Yuya Tanizaki, Yoshimasa Hidaka, Tomoya Hayata
  • Organizer: KEK Theory Workshop 2015 Dec
  • Place of Presentation: KEK(茨城県つくば市)
  • Year and Date: 2015-12-01
  • Int'l Joint Research
• [Presentation] Lefshcetz-thimble path integral for studying the Silver Blaze phenomenon (2015)
  • Author(s): Yuya Tanizaki, Yoshimasa Hidaka, Tomoya Hayata
  • Organizer: KEK理論センター研究会「原子核・ハドロン物理の課題と将来」
  • Place of Presentation: KEK（茨城県つくば市）
  • Year and Date: 2015-11-24
• [Presentation] Lefschetz-thimble method for evading the mean-field sign problem (2015)
  • Author(s): Yuya Tanizaki, Hiromichi Nishimura, Kouji Kashiwa
  • Organizer: Quark Matter 2015
  • Place of Presentation: 神戸ファッションマート（兵庫県神戸市）
  • Year and Date: 2015-09-27
  • Int'l Joint Research
• [Presentation] Dynamic critical behavior for the relativistic O(N) model in the framework of the real-time functional renormalization group and applications to QCD (2015)
  • Author(s): David Mesterhazy, Jan H. Stockemer, Yuya Tanizaki
  • Organizer: Quark Matter 2015
  • Place of Presentation: 神戸ファッションマート（兵庫県神戸市）
  • Year and Date: 2015-09-27
  • Int'l Joint Research
• [Presentation] Lefschetz-thimble path integral for solving the mean-field sign problem (2015)
  • Author(s): Yuya Tanizaki, Hiromichi Nishimura, Kouji Kashiwa
  • Organizer: LATTICE 2015
  • Place of Presentation: 神戸コンベンションセンター（兵庫県神戸市）
  • Year and Date: 2015-07-24
  • Int'l Joint Research
• [Presentation] Lefschetz-thimble法の最近の発展と物理への応用 (2015)
  • Author(s): 谷崎佑弥
  • Organizer: チュートリアル研究会「重イオン衝突の物理」
  • Place of Presentation: 理化学研究所
  • Year and Date: 2015-03-25 – 2015-03-27
• [Presentation] 実時間経路積分へのLefschetz thimble法の応用とトンネル効果 (2015)
  • Author(s): 谷崎佑弥、小池貴之
  • Organizer: 日本物理学会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2015-03-22 – 2015-03-24
• [Presentation] Lefschetz-thimble path integral and spontaneous symmetry breaking of matrix models (2015)
  • Author(s): Yuya Tanizaki
  • Organizer: Frontiers of Hadron Physics; Brain circulation workshop
  • Place of Presentation: Brookhaven National Lab. (USA)
  • Year and Date: 2015-02-25
• [Presentation] Real-time tunneling phenomena through Lefschetz-thimble path integral (2014)
  • Author(s): Yuya Tanizaki
  • Organizer: Midwest Theory Get-Together
  • Place of Presentation: Argonne National Lab. (USA)
  • Year and Date: 2014-09-05 – 2014-09-06
• [Presentation] Functional renormalization group approach for composite particle excitations (2014)
  • Author(s): Yuya Tanizaki
  • Organizer: Algebraic Methods in Quantum Field Theory
  • Place of Presentation: Sofia, Bulgaria
  • Year and Date: 2014-07-07 – 2014-07-10
  • Invited
• [Presentation] Functional renormalization group method for ultracold fermions (2014)
  • Author(s): Yuya Tanizaki
  • Organizer: RBRC seminar
  • Place of Presentation: Brookhaven National Laboratory (New York, USA)
  • Year and Date: 2014-03-06
• [Presentation] Functional Renormalization Group Method for BEC of Composite Particles (2014)
  • Author(s): Yuya Tanizaki
  • Organizer: Beyond Quasiparticles : New Paradigms for Quantum Fluids
  • Place of Presentation: Aspen Center for Physics (Colorado, USA)
  • Year and Date: 2014-01-13
• [Presentation] 非相対論的な少数系に対する汎関数繰り込み群の構造 (2013)
  • Author(s): 谷崎佑弥
  • Organizer: 日本物理学会
  • Place of Presentation: 高知大学(高知県高知市)
  • Year and Date: 2013-09-23
• [Presentation] Fermionic functional renormalization group approach to strongly coupled superfluidity (2013)
  • Author(s): Yuya Tanizaki, Gergely Fejos, Tetsuo Hatsuda
  • Organizer: XVII. International Conference on Recent Progress in Many-body theories (MBT17)
  • Place of Presentation: Steigenberger Hotel Sonne (Rostock, Germany)
  • Year and Date: 2013-09-10
• [Remarks] Yuya Tanizaki's homepage
  • URL: http://ribf.riken.jp/~tanizaki/index.html
• [Remarks] Yuya Tanizaki's Homepage
  • URL: http://ribf.riken.jp/~tanizaki/
• [Remarks]
  • URL: http://ribf.riken.jp/~tanizaki/