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BCS superfluidity in the 2D Fermi-Hubbard model NSF, Simons Foundation, AFOSR MURI, NNSFC, CAS, NKBRSFC ICTP, Oct.28, 2014

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Youjin Deng, USTC Evgeny Kozik, King’s College Boris Svistunov Umass, Amherst arXiv:1408.2088

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Fermi-liquid @ T-independent in Fermi-liquid

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What do we know with meaningful error bars MOTT, AFM FM Stripes? AFM ? ? ? ? ? ? ?

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Cooper instability in the BCS regime Fermi-liquid form at determines is temperature (and frequency) independent in the limit

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Protocol: Compute Fermi surface parameters ; verify their T-independence Transform Solve for eigenvectors and eigenfunctions Predicted divergence To determine compute correction (future work): is -independent, to leading order in small g

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up to

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p-pairing dominates only d-pairing

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Finite n: and expansion to Missed the phase for

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Dyson Equations: G&T-matrix self-consistent skeleton formulation ( contact potential ) BOLD DIAGRAMMATIC CALCULATION: Define “bare” pair propagator : ( exact solution of the two-body problem ) Skeleton diagrams In terms of “exact” or “fully dressed” propagators &

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Compensation trick: Identical representation (under integration) Original representation Arbitrary auxiliary function with “Design” it to compensate

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G&T-matrix self-consistent formulation ( contact potential ) BOLD DIAGRAMMATIC CALCULATION:

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p-d xy for U>4 T C for U<4 and n<0.7 Any dispersion relation for the same U and n For U>4.and. n>0.7 we need a different scheme SIMONS COLLABORATION ON MANY ELECTRON PROBLEM Conclusions/perspectives Zanchi, Schulz, PRB 61, 13609 (2000) d x2-y2 -AFM for U<2

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High-order (at least order-6) calculations based on fully-dressed propagators should become a norm! Only 113824 self-consistent diagrams

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Solving Equations. -132 = 4x – 5(6x – 10) -132 = 4x – 30x + 50 -132 = -26x + 50 -182 = -26x 7 = x.

Solving Equations. -132 = 4x – 5(6x – 10) -132 = 4x – 30x + 50 -132 = -26x + 50 -182 = -26x 7 = x.

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