"From a theoretical tool to the lab"

Transcription

1 N "From a theoretical tool to the lab" Aline Ramires Institute for Theoretical Studies - ETH - Zürich Cold Quantum Coffee ITP - Heidelberg University - 13th June 2017

2 ETH - Hauptgebäude The Institute for Theoretical Studies 300m 5km ETH - ITP - Established in 2013; - Interdisciplinary institute dedicated to research in mathematics, theoretical physics and theoretical computer science; - Currently: 9 Junior Fellows and 6 Senior Fellows, - Support from Dr. Max Rössler and the Walter Haefner Foundation.

3 Outline - Strongly Correlated Systems Local Moment formation and the Kondo Effect Heavy Fermions - Large-N approach Spin and Time-reversal: Symplectic-N Decoupling spin Hamiltonians - Q: Just a theoretical tool? Enlarged symmetries with ultracold atoms

4 The Periodic Table of Elements

5 The Smith-Kmetko Diagram Increasing localization Magnetism 4f 5f 3d Increasing localization Fermi Liquid FS "Electrons in the brink of localization" More localized orbitals Enhanced interactions Strong Correlations J. L. Smith and E. A. Kmetko, J. of the Less-Common Metals (1982)

6 Examples of Strongly Correlated Systems Cuprates Schematic diagram YBa2Cu3Ox Fe-pnictides Ba(Fe1-xCox)As2 Heavy Fermions CeRhIn5 Strange Metal T(K) Strange metal Fradkin, Nature Physics (2012) Tranquada, Physics 3 (2010) x Knebel, J. Phys. Soc. Jpn. (2011) Electrons in the brink of localization Easily tunable Repeating theme What can we learn from HF?

7 Localized Orbital Effective models and local moment formation Anderson Impurity Model Conduction sea Infinite-U Anderson Model H Atomic Kondo Impurity Model U+ε f -εf>0 AFM At low T only the spin DOF remains. P. Coleman, Introd. to Many Body Physics (2015) Requires:

8 Poor-man scaling and the Kondo Effect Kondo Impurity Model What if we want to keep renormalizing? D D - δd E States to be removed ρ(e) -D + δd -D States to be removed J. Kondo, Prog. in Theor. Phys. 32, 1, 37 (1964) P. W. Anderson, J. Phys. C: Solid State Phys. 3, 2436, 2 (1970) Below TK: Singlet Bound State

9 Energy Scales in Heavy Fermions Kondo Lattice Model Kondo Temperature Doniach Phase Diagram Impurity: Singlet Bound State Lattice: HEAVY Fermi Liquid RKKY Temperature AFM? QCP FL S. Doniach, Physica B (1977) J. Kondo, Prog. in Theor. Phys. 32, 1, 37 (1964) Ruderman-Kittel-Kasuya-Yosida ( )

10 Take-home messages I & II: There is a class of materials called heavy fermion systems in which electrons are very strongly interacting. The effective models to describe them usually start from a Kondo lattice model, which is written in terms of local moments and cannot be treated perturbatively.

11 Large-N Approach No natural small energy scale: Introduce an artificial small parameter: 1/N Quantum Chromodynamics Barions (N-body singlets) Condensed Matter Cooper Pairs Valence Bonds? L. Balents, Nature (2010) G. t Hooft, Nucl Phys B 71, 461 (1973) E. Witten, Nucl Phys B 160, 57 (1979)

12 Symplectic-N Approach Requirement of consistency Symplectic condition Time-reversal: Generators: Generalized Spin Operators Now we have a generalisation of spin operators which are well behaved under the time-reversal operation. R. Flint et. al., Nature (2008)

13 Decoupling Spin Hamiltonians SU(N) Symmetry SP(N) Symmetry Hopping / Hybridization Superconductivity / Valence Bonds SP(N) properly accounts for Frustration and Superconductivity!

14 Take-home messages III & IV: CeRhIn5 Large-N generalisations are useful for the description of strongly correlated materials. The symplectic-n approach seems to provide a more appropriate generalisation of spin operators Θ

15 Q: Are these models with enlarged symmetries only theoretical tools or can they be real? I feel like a heavy fermion!

16 Cold Atoms and enlarged symmetries At ultra-low temperatures and in the low density limit, we can model interacting atoms with contact interactions. Total angular momentum conservation. f: Hyperfine Spin (Total angular momentum of the atom) F: Total angular momentum of the PAIR of atoms which is scattering

17 Cold Atoms and enlarged symmetries Note that only even-f channels contribute to scattering: Taking α <-> β and using properties of the CGC: We find: So for both Bosons (η = 1 and 2f even) and Fermions (η = -1 and 2f odd): F = 0, 2, 4, 6,

18 Cold Atoms and enlarged symmetries SU(N) Symmetry Realization: Alkaline-Earth atoms Condition: SP(N) Symmetry *Naturally satisfied for in this case the interaction vertex simplifies to: Define: Number of particles in each flavour = nα, is a conserved quantity. Colour magnetization = nα-n-α is a conserved quantity. A. Ramires arxiv (2017)

19 Cold Atoms and enlarged symmetries 1) Not strong dipole-dipole interaction 2) Stable Elements 3) Fermionic Isotopes with f > 1/2 SP(6) SP(8) Dipolar character SP(10) Already Condensed Realizes SP(N) * Realizes SU(N) T. Maier, PhD Thesis (2015)

20 Take-home messages V & VI: It is possible to realise systems with enlarged symmetries in cold atomic systems SP(N) is a current challenge for experimentalists.

21 Conclusion - Motivated by heavy fermion systems - Looked for appropriate theoretical tools: Symplectic-N - Q: Are these models with enlarged symmetries real? - Cold atoms can realise SU(N) and SP(N) symmetries I feel like a heavy fermion!