ISIS Facility, STFC Rutherford Appleton Laboratory

Functional Materials Group

Hubbard Theory Consortium

VIVALDO L. CAMPO, JR (1), KLAUS CAPELLE (2), CHRIS HOOLEY (3), JORGE QUINTANILLA (4,5), and VITO W. SCAROLA (6)

(1) UFSCar, Brazil, (2) UFABC, Brazil, (3) SUPA and University of St Andrews, UK, (4) SEPnet and Hubbard Theory

Consortium, University of Kent, (5) ISIS Facility, Rutherford Appleton Laboratory, and (6) Virginia Tech, USA

SCES 2011, Cambridge, 1 September 2011

Double occupancy as a probe of the Mott transition for fermions in one-dimensional

optical lattices

arxiv.org:1107.4349

Context: Experiments on 3D Hubbard model

Experimental evidence for the Mott transition:

U. Schneider, L. Hackermuller, S. Will, Th. Best, I. Bloch, T. A. Costi, R. W. Helmes, D. Rasch, A. Rosch, Science 322, 1520-1525 (2008).

Robert Jordens, Niels Strohmaier, Kenneth Gunter, Henning Moritz & Tilman Esslinger, Nature 455, 204-208 (2008).

Problem:What will happen in 1D?

• Hamiltonian:

• Evaluate double occupancy:

Bulk 1D Hubbard model (no trap)

Elliott H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968); 21, 192 (1968).

f

0 1 2

U / t

Luttinger Liquid

Mott insulator:

Finite temperature• Use high-temperature expansion:

(must go at least to 2nd order)• Double

occupancy:

= + + ...

Finite temperature

• Match to low-T expansion from quantum transfer method [Klümper and Bariev 1996]

• Obtain

• C(x) is the unity central charge from CFT for the Hesienberg universality class:

Finite temperature• Very good match between

high-T and low-T expansions.• d vs T is non-monotonic

(suggests cooling mechanism with 1D system as reference state)

• A local picture accounts well for the observed behaviour:

Effect of the trap – no fluctuations

Effect of the trap – no fluctuations

Mott insulator

Band+Mott

Band insulator D

D

• Evaluate D in the local density approximation:

D() = = j Dno trap(+½x2) U/t = 4,5,6,7

U/t = 0

Add quantum fluctuations

Quantum + thermal fluctuations

In summary...

• Fermionic Hubbard model in one dimension.• Mott phase has inherent double occupancy

fluctuations.• Mott phase detectable via double occupancy.• Can read out double occupancy in the bulk from the

trapped data. • Non-monotonic temperature dependence – may be

used for cooling.

THANKS!arxiv.org:1107.4349