double occupancy as a probe of the mott transition for fermions in one- dimensional optical lattices
DESCRIPTION
Contributed talk at SCES 2011, Cambridge. We study theoretically double occupancy D as a probe of the Mott transition for trapped fermions in one-‐dimensional optical lattices and compare our results to the three-‐dimensional case. The ground state is described using the Bethe Ansatz in a local density approximation and the behavior at finite temperatures is modelled using a high-‐temperature series expansion. In addition, we solve analytically the model in the limit in which the interaction energy is the dominant energy scale. We find that enhanced quantum fluctuations in one dimension lead to increased double occupancy in the ground state, even deep in the Mott insulator region of the phase diagram (see figure). Similarly, thermal fluctuations lead to high double occupancies at high temperatures. Nevertheless, D is found to be a good indicator of the Mott transition just as in three dimensions. Moreover, unlike other global observables, the bulk value of D in the Mott phase coincides, quantitatively, with that of a suitably-‐prepared trapped system. We discuss possible experiments to verify these results and argue that the one-‐dimensional Hubbard model could be used as a benchmark for quantitative quantum analogue simulations.TRANSCRIPT
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