Quantum entanglement for tensor product states and numerical renormalization groups

• Project/Area Number: 23540442
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Niigata University
• Principal Investigator: OKUNISHI Kouichi 新潟大学, 自然科学系, 准教授 (30332646)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: テンソル積 / くりこみ群 / エンタングルメント / テンソル積状態 / 数値くりこみ群 / 密度行列

Research Abstract

Recently, the numerical renormalization group based on the tensor product state plays a fundamental role in analyzing the ground state of the quantum many body system.We firstly clalified that the key mechanizm of the Wilon-type renromalization group is in the scale free property of the energy scale. We next found out that the fixed point structure of the higher order tensor renormalization group can be explained by doubling of the corner transfer matrix in the off critical region. We also clarified that this result is basically universal for both of the one-dimensional quantum system and two dimensional classical systems.

Research Products

• [Journal Article] Fine-Tuning of Magnetic Interactions in Organic Spin Ladders (2014)
  • Author(s): H. Yamaguchi
  • Journal Title: Journal of Physical Society of Japan Volume: 83 Issue: 3 Pages: 33707-33707
  • DOI: 10.7566/jpsj.83.033707
  • Peer Reviewed
• [Journal Article] Doubling of Entanglement Spectrum in Tenor Renormalization Group (2014)
  • Author(s): Hiroshi Ueda, Kouichi okunishi, Tomotoshi Nishino
  • Journal Title: Phys. Rev. B Volume: 89 Issue: 7 Pages: 1-10
  • DOI: 10.1103/physrevb.89.075116
  • Peer Reviewed
• [Journal Article] Collapse of Magnetic Order of the Quasi One-Dimensional Ising-Like Antiferromagnet BaCo_2V_2O_8 in Transverse Fields (2013)
  • Author(s): Shojiro Kimura, Koichi Okunishi, Masayuki Hagiwara, Koichi Kindo, Zhangzhen He, Tomoyasu Taniyama, Mitsuru Itoh, Keiichi Koyama, and Kazuo Watanabe
  • Journal Title: Journal of the Physical Society of Japan Volume: vol.82 Issue: 3 Pages: 0337061-4
  • DOI: 10.7566/jpsj.82.033706
  • Peer Reviewed
• [Journal Article] Magnetic field-induced phase transitions in the S=1/2 two-leg spin-ladder material Cu(DEP)Br2 (2012)
  • Author(s): Z. Honda, H.A. Katori, M. Ikeda, M. Hagiwara, K. Okunishi, M. Sakai, T. Fukuda, N. Kamata
  • Journal Title: Journal of Physical Society of Japan Volume: 81 Issue: 11 Pages: 113710-4
  • DOI: 10.1143/jpsj.81.113710
  • Peer Reviewed
• [Journal Article] Spin-chirality separation and S3-symmetry breakings in the magnetization plateau of the quantum spin tube (2012)
  • Author(s): Kouichi Okunishi, Masahiro Sato, Toru Sakai, Kiyomi Okamoto, and Chigak. Itoi
  • Journal Title: Phys. Rev. B Volume: 85 Issue: 5 Pages: 54416-54416
  • DOI: 10.1103/physrevb.85.054416
  • Peer Reviewed
• [Journal Article] Novel Phase Transition Probed by Sound Velocity in Quasi-One-Dimensionial Ising-Like Antiferromagnet BaCo2V2O8 (2011)
  • Author(s): H.Yamaguchi
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 3 Pages: 33701-33701
  • DOI: 10.1143/jpsj.80.033701
  • Peer Reviewed
• [Presentation] 数値くりこみ群の発展-DMRGからMERA まで (2014)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 東海大学
  • Year and Date: 2014-03-27
  • Invited
• [Presentation] 数値くりこみ群の発展‐密度行列くりこみ群からMERAまで (2014)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 東海大学
  • Invited
• [Presentation] bilinear-biquadratic スピン鎖の負符号問題II (2013)
  • Author(s): 奥西巧一, 他
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 徳島大学
  • Year and Date: 2013-09-26
• [Presentation] bilinear-biquadratic 鎖の負符号問題 (2013)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 広島大学
  • Year and Date: 2013-03-26
• [Presentation] bilinear-biquadraticスピン鎖の負符号問題II (2013)
  • Author(s): 奥西巧一，原田健自
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 徳島大学
• [Presentation] bilinear-biquadratic鎖の負符号問題 (2013)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会
  • Place of Presentation: 広島大学
• [Presentation] Wilson 数値くりこみ群の場の理論化 (2012)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2012-09-14
• [Presentation] 数値くりこみ群アルゴリズムとエンタングルメント (2012)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2012-09-14
  • Invited
• [Presentation] Quantum phase transitions in 1/3 plateau of quantum spin tube (2012)
  • Author(s): 奥西巧一
  • Organizer: 国際磁性学会議
  • Place of Presentation: プサン国際会議場
  • Year and Date: 2012-07-13
• [Presentation] Wilson 数値くりこみ群とエンタングルメント (2012)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2012-03-26
• [Presentation] Quantum phase transitions in 1/3 plateau of the quantum spin tube (2012)
  • Author(s): Kouichi Okunishi
  • Organizer: 国際磁性学会議（ICM）
  • Place of Presentation: プサン国際会議場
• [Presentation] Wilsonの数値繰り込み群の場の理論化 (2012)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会
  • Place of Presentation: 横浜国立大学
• [Presentation] 数値的くりこみ群アルゴリズムとエンタングルメント (2012)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会
  • Place of Presentation: 横浜国立大学
  • Invited
• [Presentation] Wilson数値繰り込み群とエンタングルメント (2012)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 関西学院大学
• [Presentation] スピンチューブのプラトー状態での内部対称性と新奇秩序の数値的研究 (2011)
  • Author(s): 奥西巧一, 他
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 富山大学
  • Year and Date: 2011-09-22
• [Presentation] VBS 状態のDisentanglerII (2011)
  • Author(s): 奥西巧一, 他
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 富山大学
  • Year and Date: 2011-09-21
• [Presentation] VBS状態のDisentangler II
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 富山大学