01/20 E or J KT , et al. PRB 2017; PRB 2017 KT and M.Sato arXiv 2018 Z. Gong, …, KT , … PRX 2018 Poster-12 兎子尾 KT et al. in preparation Poster-31 山本
02/20 Lightning ( 雷 ) Lichtenberg figure Zener diode Plasma display Figures from Wikipedia
03/20 c.f. Bloch’s theorem, 1928 Gap Gap Zener diode Tunneling between Bloch bands
04/20 Mott E U Bias Voltage Experimental observation Theoretical studies Current E Electric field Yamakawa et al., Y. Taguchi et al., PRB 2000 Oka, Arita and Aoki, PRL 2003 Nat. Mat. 2017
05/20 E E E T p e Schwinger 機構 ( 電子 - 陽電子対生成 ) Current C. Sow et al., Science 2017
06/20 ・ ・ c f Fermionic Mott ins. CDW insulators Kondo insulators Bose Mott insulators Universality in breakdown (Noneq . phase transition)… ? ・ c.f. : Analytical : Numerical(DMRG) Fermionic Hubbard (1D) Integrable (Bethe ansatz) Oka and Aoki, PRB 2010
06/20 ・ ・ c f Fermionic Mott ins. CDW insulators Kondo insulators Bose Mott insulators Universality in breakdown (Noneq . phase transition)… ? ・ c.f. : Analytical : Numerical(DMRG) Fermionic Hubbard (1D) Integrable (Bethe ansatz) Oka and Aoki, PRB 2010
07/20 KT , M. Nakagawa, N. Kawakami, in prep. Threshold Insulator Metal I F F th
08/20 c.f. T. Oka and H. Aoki, PRB 2010 Excited states 1st ex. G.S. G.S.
Outline
Outline
09/20 H ( t ) Dykhne-Davis-Pechukas (DDP) 公式 Dykhne, Sov. Phys. JETP 1962 Davis and Pechukas, J. Chem. Phys. 1976 “Critical time”
10/20 : Landau-Zener model E t “Critical time” ReE t c Re t Im t LZ formula
Outline
11/20 Setup: , Threshold F F th A= ih
12/20 A= ih c.f. Random potential → Hatano-Nelson model Hatano and Nelson, PRL 1996 c.f. Hubbard case: (proposed by Fukui and Kawakami) Fukui and Kawakami, PRB 1998 Energy gap e +h Gap closing =Mott breakdown e -h h (Asymmetry) h c
12/20 A= ih c.f. Random potential → Hatano-Nelson model ・非対称ホッピングの冷却原子系での実現提案 Hatano and Nelson, PRL 1996 ・非エルミート系におけるトポロジカル相 c.f. Hubbard case: (proposed by Fukui and Kawakami) [Ref. Z. Gong, …, KT , … ,M. Ueda, Phys. Rev. X 8 031079 (2018)] Fukui and Kawakami, PRB 1997 Energy gap e +h Gap closing =Mott breakdown e -h h (Asymmetry) h c
Outline
13/20 h (Asymmetry) h c c.f. Giamarchi’s text book
14/20 Sine-Gordon |g|
15/20 Main result
16/20 ドープされたエルミートな絶縁体へマップされた
17/20 h c h *Schematic figures ,
18/20 Analytic formula of threshold field Landau-Zener E t β=2 : Band insulator interaction velocity 2. 具体的な模型ではなく有効場の理論にのみ依る
19/20 Check: Band insulator (SSH) CDW insulator (XXZ) Fermionic Mott (Hubbard) /Δ 0 弱結合領域で幅広く成立している
20/20 KT , M. Nakagawa, N. Kawakami, in prep. Threshold Insulator Metal I F F th
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