brief outline

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brief outline

• Lattice definitions interest of the problem
• experiments on JJAs opt. lattice proposal
• Bose-Hubbard model Quantum Rotor limit
• Tools to tackle the problem
• Analytic approaches
• mean field Ginzburg-Landau
• strong coupling expansion
• Numeric MonteCarlo approach
• effective action as (21)D XY model
• Magnetic frustration
• localization of single particle states (AB cages)
• superconductivity at high tunnelling
• intermediate phase without disorder !?

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reasons of Interest

• BH model to study strongly correlated systems
• JJAs Opt.Latt. are ideal models to study it
  easy tunability!

COUPLINGS SCALAR FRUSTR. VECTORIAL FRUSTR.
OPT. LATT. laser intensity chem. potential rotation/ internal states
JUNCT. ARRAYS grain dimension/ barrier thickness electrostatic gates magnetic fields
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MC unfrustrated results
Modulation in phase localization
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MC full magn. frustr. (2)
Symbols Lt 6, 12, 30 Fillings Lx 6, 12,
18 Fixed ratio Lt2/3 Lx
Dependence on Lt ... not on spatial Lx x Ly !
Gap closed but no spatial correlation
Dyn. crit. exp. z0 gives independence of
correlation lengths ? 1D to 3D crossover
mechanism ?
Unfortunately not big enough system to decide
(frustration make thermalization hard)
Data corresponds to 1/K from 0.6 to 0.75 with
steps 0.025
Scaling on Lt seems to leave a window
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Open questions
Is there an intermediate phase between Mott and
superfluid ?
Which is the correct scaling behaviour of
stiffness and compressibility, since bands of
gauge-link matrix are flat and GLW analysis says
z 0 !?
OUR IDEA single particle correlation lengths may
be independent in time and space and the
intermediate state we observe can be due to a 1d
to 3d crossover due to finite size of the systems
we are considering in simulations
MOREOVER How are results affected by the great
degeneracy of ground states?
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summary

• T3 (dice) planar, Bravais lattice, no disorder
  but peculiar link matrix with diff. coord.
• Bose Hubbard Quantum Rotor
• Mapping into (21)D XY model
• Magnetic frustration
• Aharanov Bohm cages for single particles
• probable pair of pairs superfluidity
• intermediate strange phase without disorder !?
• crossover mechanism? new scaling laws?

MR, V. Cataudella, and R.Fazio, Phys Rev. B 73,
144511 (2006) Phys. Rev. B 73, 100502R (2006)