1. A new scenario for the metal- Mott insulator transition in 2D Why 2D is so special ? S. Sorella Coll. F. Becca, M. Capello, S. Yunoki Sherbrook 8 July 2005 1 Critical behavior near a two dimensional Mott insulator

2. The still unexplained phase diagram A huge non-Fermi liquid region close to a Mott insulator ? 2

3. The variational Jastrow-Slater correlation mean field 3

4. The Gaskell-RPA solution Within the same RPA the structure factor is: 4

5. In a lattice model with short range interaction? And the f-sum rule? Thus no way to get an insulator with Jastrow-Slater? See e.g. Millis-Coppersmith PRB 43, (1991).

6. M. Capello et al. PRL 2005 The 1d numerical solution U/t=4 L=82 5

7. A long range Jastrow correlation can drive a metallic Fermi sea to a Mott insulator!! 6 For an insulator : No charge stiffness Incompressible fluid

8. What in higher dimension? Brinkmann-Rice : 7

9. Infinite dimension (DMFT) The insulator is more realistic 8

10. Now we can do the same in 2D (obviously we neglect AF as in DMFT or in BR) KT means Kosterlitz-Thouless transition point, explained later… 9

11. A clear transition is found 10

12. Feynmann never lies (assumed) Excitation energy induced by where is the exact ground state of a physical Hamiltonian The reason is simple Exact eigenstate 11

13. Now let us start from the insulator Doblon holon Singly occupied 12

14. Quantum Classical For large U/t we are in the very dilute regime Mapping to a classical model 13

15. Now ask how can we satisfy No way out, for any insulator U>>t (any D): In 2D a singular v between holon and doblon 14

16. Exact mapping to the 2D CG model We can classify all 2D insulators in terms of true 2D Mott Insulator (no broken translation symmetry) 15

17. A KT transition is found 16

18. In the “plasma phase”, similar to Luttinger liquid: Fermi surface but no Fermi jump Similar conclusions in Wen & Bares PRB (1993) 17

19. Instead in the confined phase The density matrix appears to decay exponentially i.e. the momentum distribution is analytic in k 18

20. Anomalous exponents for Z in 2D t-J (projected wf) Hubbard 19 Prediction HTc:

21. From 2D Coulomb gas (see P. Minnhagen RPM ’87) : The charge correlation decays as power law > 4 because A>0  there is a gap at q  0 according to Feynmann  correlations are decaying as power laws A gap with power laws !!! 20 n.b. This implies that any band insulator  plasma phase

22. It looks consistent, though it is impossible to prove numerically 21

23. Clearly quadratic No Friedel oscillations (Mott insulator) 22

24. Fermi liquid Non Fermi liquid Mott Insulator critical point New scenario T=0 D=2 (compatible with VMC on Hubbard) The Hubbard gap: Consistent with DMFT 23

25. Fermi liquid Non Fermi liquid Mott Insulator (or d-wave BCS) incompressible (with preformed pairs) Even more new scenario T=0 D=2 (long range interactions?) A charge gap opens up continuously 24

26. In the plasma phase for we have: 1)Z  0 Non Fermi liquid, singular at 2) No d-wave ODLRO (preformed pairs at T=0) pseudogap T=0 phase ( ) 25

27. Conclusions A Mott transition is found in 2D Hubbard (VMC) Mapping to 2D Coulomb gas confined phase= Mott insulator plasma phase=Non Fermi liquid metal Critical Z  0 in the insulating/metallic phase Power law correlations in the insulator with gap Non Fermi liquid phase possible in 2D? 26

28. D-wave SC Non Fermi liquid Mott Insulator with preformed pairs Finite doping ?