Boris Svistunov Nikolay Prokof’ev (UMass) Lode Pollet (ETH) Massimo Boninsegni (U of Alberta)...

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’