Boris Svistunov Nikolay Prokof’ev (UMass) Lode Pollet (ETH) Massimo Boninsegni (U of Alberta) Matthias Troyer (ETH) Anatoly Kuklov (CUNY) PITP-The Outing.

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?

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.

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’

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

Feynman’s path integral (world line) representation of quantum statistics

0

1/T

-Tre HZ

spatial coordinate

Worldline winding numbers and superfluidity

0

1/T

0

0W 1W

2 2/ dS W L Pollock and Ceperley,

PRB 36, 8343 (1987).

1/T

Two sectors of the configuration space

0

1/T

0

1/T

† -2 2 1 1†

1 1 2 2 2 2 1 1 -

Tr , , e, ; , , ,

Tre

H

HG

r rr r r r

† -2 2 1 1Tr , , e H

r r-Tre HZ

Z-sector G-sector

Green’s functionin Matsubara representation

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

Bosonic insulating ground sates do exist

(path-integral argument)

Renormalization: worldlines and lattice cites annihilate each other

0

1/T

Insulator (if exists)

Renormalization: more detail

0

1/T

, , length; 0 with increasing interactionQ QF E T S E S T

(Pseudo-)thermodynamic favorability of a vacancy (interstitial) worldline

Conclusion: No vacancy/interstitial worldlines at strong enough interaction.

‘quantum temperature’

vacancy wordline

0

1/T

‘Free energy’ ofthe worldline

HCP He-4 crystal is a clear-cut insulator

melting curve

Map of the condensate wave function reveals the superglass

10 slices across the z-axis

3o

0.0359A 0.2 800

n T K N

4 1 910 10 srelax Dt (a rough estimate)

0.07(2)S

(The superglass state is obtained by quenching.)

Superglass state of He-4

o

(A)ro

(A)r

log of single-particle density matrix density-density correlator10

3o

0.0359A 0.2 800

n T K N

0.07(2)S

Superluidity of grain boundaries and more:

in the talk by Lode Pollet

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%.

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

/mR

/mR

Screw dislocation in He-4 hcp crystal

Superfluidity in dislocation network. Shevchenko state vs ‘vortex liquid’

l

, / , 1 /CF E TS E a l S T a l

Sergei Shevchenko,

Sov. J. Low Temp. Phys., 1987, 1988

Free energy perphase-twist

1/ 23

* * */ / , 1DC ST T a l T n n T K

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.

*CT T T

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’