1. Boris Svistunov Nikolay Prokof’ev (UMass) Lode Pollet (ETH) Massimo Boninsegni (U of Alberta) Matthias Troyer (ETH) Anatoly Kuklov (CUNY) PITP-The Outing Lodge, 2007 What Do We Know of Bosonic Groundstates?

2. Non-triviality of bosonic groundsates (from the quantum-field-theoretical viewpoint) 1.Superfluid – Almost trivial: Equivalent to a classical field (BEC). 2.Supersolid – Quite simple: Equivalent to a modulated BEC. 3.Insulator – Non-trivial: A strongly correlated, essentially quantum state.

3. Outline What is a supersolid from theoretical point of view? Path integral (world line) representation, worm algorithm Existence of bosonic insulating groundstates (Attn: P.W. Anderson) HCP He-4 crystal as a clear-cut insulator The superglass of He-4 Experimental evidence in favor of disordered scenarios Experimental evidence against non-superfluid scenarios Superfluid dislocations. Shevchenko state vs ‘vortex liquid’

4. Two general statements about supersolid state of matter 1. Theorem: No supersolidity without either vacancies, or interstitials, or both. 2. Corollary: Continuous-space supersolids are generically incommensurate. Loosely speaking, a supersolid is always like a sponge (normal solid component) soaked with a liquid (superfluid component). Qualitatively, there is no alternative to the Andreev-Lifshitz-Chester scenario. Prokof’ev and BS, 2005

5. Feynman’s path integral (world line) representation of quantum statistics spatial coordinate

6. Worldline winding numbers and superfluidity Pollock and Ceperley, PRB 36, 8343 (1987).

7. Two sectors of the configuration space Z-sectorG-sector Green’s function in Matsubara representation

8. Worm updates Boninsegni, Prokof’ev, and Svistunov (2006)

9. Bosonic insulating ground sates do exist (path-integral argument)

10. Renormalization: worldlines and lattice cites annihilate each other Insulator (if exists)

11. Renormalization: more detail

12. (Pseudo-)thermodynamic favorability of a vacancy (interstitial) worldline Conclusion: No vacancy/interstitial worldlines at strong enough interaction. ‘quantum temperature’ vacancy wordline ‘Free energy’ of the worldline

13. HCP He-4 crystal is a clear-cut insulator melting curve

14. Map of the condensate wave function reveals the superglass 10 slices across the z-axis (a rough estimate) (The superglass state is obtained by quenching.)

15. Superglass state of He-4 log of single-particle density matrix density-density correlator 10

16. Superluidity of grain boundaries and more: in the talk by Lode Pollet

17. Experimental evidence in favor of disordered scenarios S. Rittner and J. Reppy, 2006-2007 E. Rudavskii and collaborators, 2007 M. Chan and collaborators, 2007 1.The effect disappears with annealing, or at least gets as small as 0.03%. 2.The amplitude of the effect depends on cooling protocol, and can be as large as ~20%.

18. Experimental evidence against non-superfluid scenarios 1. No effect in C-shape cell. 2. Crucial diffrence between He-4 and He-3. 3. ‘Critical velocity’ is the same with and without Vycor, being 4. Recent results by H. Kojima and collaborators: (i)No frequency dependence (ii)Critical velocity depends on protocol and can be made at least two orders of magnitude larger than

19. Screw dislocation in He-4 hcp crystal

20. Superfluidity in dislocation network. Shevchenko state vs ‘vortex liquid’ Sergei Shevchenko, Sov. J. Low Temp. Phys., 1987, 1988 Free energy per phase-twist Shevchenko state is the normal state with anomalously suppressed dissipative properties. It takes place in the temperature interval, where the only dissipative mechanism is due to quantum phase slipages.

21. Conclusions HCP He-4 crystal is a clear-cut insulator Insulating bosonic groundstate does exist Superglass, an amorphous supersolid The core of screw dislocation is superfluid. Shevchenko state behaves like ‘vortex liquid’