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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’