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Role of quantal phases in low-dimensional correlated electrons -nonperturbative approach

Talk at National Center of Theoretical Sciences, Hsinchu, Taiwan Feb.1, 2002. Role of quantal phases in low-dimensional correlated electrons -nonperturbative approach. Computational Materials Research Center National Institute for Materials Research ( 物質・材料研究機構 )

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Role of quantal phases in low-dimensional correlated electrons -nonperturbative approach

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  1. Talk at National Center of Theoretical Sciences, Hsinchu, Taiwan Feb.1, 2002 Role of quantal phases in low-dimensional correlated electrons-nonperturbative approach Computational Materials Research Center National Institute for Materials Research (物質・材料研究機構 ) Akihiro TANAKA（田中秋広）, Xiao Hu(胡暁) http://www.nims.go.jp/cmsc/scm/index.html

  2. Outline of Talk 1.Examples of quantal (Berry) phases for spins: -quantum tunneling in nanomagnets and JJ s 2.Impurity effects in spin gapped systems and superconductivity: -role of quantal phases 3. Related physics in stripes in superconductors

  3. What is the Berry phase of a spin? …it records the history of its directional fluctuation. ω Quantization of spin follows from ambiguity of ω mod 4π: Geometric nature of Berry phases can lead to far-reaching consequences.

  4. Illustration: tunneling in nano-size molecular magnets eg. Ｆｅ 8 (Wernsdorfer et al, Science 284, 133 (1999)) Ｍｎ１２ acetate (S=10)(Wernsdorfer et al cond-mat/0109066) consider an easy-plane easy-axis magnet z Path B Path A |2> Tunneling amp. between the 2 low energy states y |1> x ■Amp=0 for half-integer S : destructive interference between paths A, B ⇒ absence of splitting of the classical levels ■For integer S: constructive interference

  5. θ Φ Application to Josephson junctions (lattice superconductor) pseudo-spin (S: controlled by gate-voltage) description of JJ arrays Charging energy Ec →Kz Josephson energy EJ→Ky For large Ec: continuum notation The spin tunneling analysis can be carried over to the Cooper pair tunneling problem. “Geometrically controlled quibits” Makhlin et al Rev. Mod. Phys. 73, 357(2001).

  6. Competing/Coexisting Orders in Correlated Electrons 物質・材料研究機構 (NIMS) 田中秋広、胡暁 http://www.nims.go.jp/cmsc/scm/index.html □MC simulation of SO(5) theory of high Tc superconductivity □Nonmagnetic impurity effects and quantal phase interference

  7. Acknowledgments to: Tokyo: N.Nagaosa，H.Fukuyama，M.Saito K. Uchinokura Tsukuba: M. Hase, N. Taniguchi, T. Hikihara

  8. Experiments and Backgrounds 1. Nonmagnetic impurity in singlet spin-gapped systems ■Spin-Peierls compound CuGeO3 AF with less than 1%Zn (Si, Mn)doping ■Spin-ladder compound SrCu2O3 AF order with ～1% Zn doping(Azuma et al ’９７） ■Pseudo-gap phase of underdoped cuprates Cu→Zn subst. in YBCO; weight transfer to low energy (Kitaoka et al ’93) before Basic picture after Masuda et al (CuGeO3)

  9. Questions These analogies have received attentions: ■Sensitivity of 40meV magnetic resonance mode to Cu→Zn subst. (Keimer, Fukuyama) ■Zn doping into staggered flux state (Pepin and P.A.Lee) Butviewing impurities (site depletion)as the static limit of mobile holes, what information can this provide for the hole-doped system and its SC?

  10. 2. Spin-Peierls like (bond-centered density) order in underdoped cuprates? Softening of LO phonon at q=(π/2,0,0) McQueeney et al PRL 82 (1999)628(La 1.85 Sr 0.15 CuO4) & unpublished 2001(YBa2Cu3O 6.95 ) questions: ■ role of AF fluctuation on stripes? ■relation to superconductivity?

  11. Step2: t’-type hopping + intersublattice attraction A by-productSU(2) invariant phase-Hamiltonian approach System quasi-1d spin-Peierls state Same origin: spin-charge phase interference Static vacancy→induced AF Mobile vacancy(hole)→superconductivity Findings Step1: local weight transfer: singlet→AF

  12. The Main Idea In a non-singlet state (SDW+directional fluctuations), In a singlet state, the spin moments are quenched (no “arrows”)-> Berry phase effects should be absent Conventional bosonization: does not give complete description of Semiclassical methods: can only immitate as Wanted: a method which incorporates both including space and/or time nonuniformity of singlet pair formations （e.g. RVB）

  13. Sugawara form : Hamiltonian for free fermion U(1) SU(2) directional fluctuations

  14. Starting Hamiltonian (Peierls-Hubbard model) Semiclassical decoupling (SDW) Linearize: 4x4 Dirac fermion

  15. 2i-1 2i+3 2i a 2i+1 2i+2 ◆Physical picture (valid for ξspin>>a) Minima of spin-dependent effective potential when Q≡σZ A bond-centered density wave

  16. Generalization of phase Hamiltonians charge Phase fields spin ... Replacement See eg. A. Tsvelik’s textbook Parametrization of level 1 SU(2)WZW field as More rigorous identification:view as chiral transform:

  17. Abelian bosonization vs Rotating frame bosonization comparision of dictionaries: ■charge same ■spin ■free fermion action

  18. ・・・densityof instantons If interaction pins φ+　→　O(3)NLσ-like model +θ-term Bulk case 2 ways to treat interaction: < semiclassical > backscattering incorporated < > spin-singlet unfixed:RVB (Inagaki-Fukuyama) Vacancy: depleted charge local spin moment How will this effect the Berry phase term?

  19. Neel I[θcl=π→unfixedθ( RVB like)] Φ+ SP I[θcl=Φ-sinΦ→θ=0] Neel II[θcl=-π→unfixedθ( RVB like)] Physical View of the Spin Phase Field direct relation to θ-angle(Haldane gap physics) SP II [θcl=Φ-sinΦ+2π→θ=2π] Neel ISP I Neel IISP II

  20. Effectof dilute vacancies Put : Implement sublattice structure via2 charge fields . If 1)Static vacancies Berry phase Random exchange model(c.f. spin ladder case: Nagaosa et al) Spin correlation ξ～T-2α(α～0.22),χunif～1/T,χstagg～1/T1+2α Spectral weight transfer SP2 SP1 c.f. Saito, Saito-Fukuyama

  21. 2)mobile vacancies (holes) Terms related to : cf. Shankar Refermionize (spinless fermions): spin gauge field Enhanced intrasublattice hopping (t’-term) Effective attraction between A-holes and B-holes : can be shown to be massive Singlet pairing susceptibility~1/r

  22. FET technique may provide realization of superconductivity In quasi-1d. Attempts are now being made for CuGeO3.

  23. What can be said for 2d systems? Stripe order, AF fluctuations and Superconductivity Zhou et al, Noda et al, Science 286, 265 (1999) ARPES: low energy=stripes, high energy=dSC-like Zaanen et al,D.H.Lee: SC-stripe duality question: how can nodal fermions arise from stripes? Momoi: melting transition of stripes via dislocations AF Merons with winding number Qxy=1/2

  24. How to calculate momentum carried by AF topological defects eg. 2d Heisenberg model View [11] direction as time. → maps into 1+1d AF chain. T[11]=exp(iPa) =exp(i2πSQxy) X’ τ X’ X’ Preliminary results on similar methods applied to stripes suggest that condensation on AF merons are related to nodal fermions .

  25. Conclusion: Disorder-induced AF in spin-gapped systems: direct relation to pairing via spin-gauge field when doped with dilute amount of holes. Relevance to Underdoped Cuprate c.f. McQueeny et al : coexistence of SP order and d-wave SC (LSCO and YBCO ) Spin-Peierls compound CuGeO3 (FET?) Spin Ladder SrCu2O4 c.f. Y2BaNiO5 (Ito et al 2001) disorder induced AFLRO X enhanced conductivity X (charge gap~spin gap) Quantum melting of stripes via AF fluctuations can be related to nodal structures of the dSC.

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