1. DISORDER AND INTERACTION: GROUND STATE PROPERTIES of the DISORDERED HUBBARD MODEL In collaboration with : Prof. Michele Fabrizio and Dr. Federico Becca Maria Elisabetta Pezzoli work done in SISSA - Trieste Rutgers University

2. ● AIM: interplay of disorder and interaction in 2 D Hubbard model ● METHOD: variational wave function within VMC ● RESULTS : transition from Anderson to Mott Insulator paramagnetic and magnetic phase diagram OUTLINE

3. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 3 WHY DISORDER AND INTERACTION ?

4. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 4 Kravchenko et al., Phys. Rev. Lett. 84, 2909 Punnoose et al. Science 310, 289 (2005) CAN INTERACTION CREATE AN EXTENDED STATE IN 2D ? METAL-INSULATOR TRANSITION IN 2D

5. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 5 COLD ATOMS IN OPTICAL LATTICES ARE A UNIQUE TOOL FOR HIGLY CONTROLLED INVESTIGATIONS OF MANY BODY SYSTEMS ANDERSON LOCALIZATION in COLD ATOMS Nature, 453, 891 Nature, 453, 895 (2008 )

6. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 6 U MOTT INSULATOR (magnetic ?) D METAL ANDERSON INSULATOR ? DISORDERED HUBBARD MODEL 2 dimensions half filling

7. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 7 VARIATIONAL WAVE FUNCTION DIAGONALIZE Disordered wave function with Jastrow correlation D≠0 ANDERSON INSULATOR U=0 MOTT INSULATOR (magnetic ?) D=0 U METAL M.Capello, et al. Phys. Rev. Lett 94, 026406 (2005)

8. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 8 ANDERSON INSULATOR U MOTT INSULATOR ENERGY COMPETITION DO S U

9. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 9 A verage energy of an excitation : (f-sum rule) HOW CAN WE DISTINGUISH BETWEEN A MOTT AND AN ANDERSON INSULATOR ? Static structure factor The properties of excitations of a system are reflected in a different arrangement of the electrons in the ground state charge gap 0 MOTT INSULATOR charge gap = 0 ANDERSON INSULATOR Kohn, Phys. Rev. 133, A171 (1964)

10. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 10 D = 5 U THE PARAMAGNETIC PHASE DIAGRAM L=98 5 8.512

11. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 11 U average over different disorder realizations PARAMAGNETIC ANDERSON INSULATOR U c = 11.5 t PARAMAGNETIC MOTT INSULATOR The Anderson-Mott transition What is the behaviour of N q disconnected ? compressibility fluctuations ORDER PARAMETER !! N q disc vs U L=98

12. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 12 EFFECTIVE DISORDER U=5 INTERPLAY BETWEEN DISORDER AND INTERACTION (our results)

13. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 13 Single particle wave function COMPLETELY LOCALIZED STATE: PLANE WAVE: INTERPLAY BETWEEN DISORDER AND INTERACTION (our results)

14. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 14 ANDERSON INSULATOR MOTT INSULATOR U PARAMAGNETIC ANDERSON INSULATOR MOTT AF D INTERMEDIATE PHASE localized states gap = 0 AF order MAGNETIC PHASE DIAGRAM

15. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 15 LOCAL MAGNETIC MOMENTS Presence of local magnetic moments at T=0 Local magnetic moments appear before the onset of long-range order: rare events Hirsch et al., Phys. Rev. Lett. 68, 1418 Paalanen et al., Phys. Rev. Lett. 57, 2061 EXPERIMENTS on (Si:P) For a review on quantum Griffiths effects: Thomas Vojta arXiv: 1005.2707v1

16. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 16 FURTHER DEVELOPMENTS What (and how) can we say about the full many body wave Function ? Is it localized or extended? Local moments: are they dominating the thermodynamics of the system? Thank you

17. Maria Elisabetta Pezzoli- BEC workshop Nice 2010 17 L=98 IPR SCALING NON MONOTONIC BEHAVIOUR OF THE JASTROW

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