A new scenario for the metal-Mott insulator transition in 2D

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A new scenario for the metal-Mott insulator
transition in 2D
Critical behavior near a two dimensional Mott
insulator

• Why 2D is so special ?

S. Sorella Coll. F. Becca,
M. Capello, S. Yunoki
Sherbrook 8 July 2005
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The still unexplained phase diagram
A huge non-Fermi liquid region close to a Mott
insulator
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The variational Jastrow-Slater
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The Gaskell-RPA solution
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In a lattice model with short range interaction?
And the f-sum rule?
Thus no way to get an insulator with
Jastrow-Slater? See e.g. Millis-Coppersmith PRB
43, (1991).
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The 1d numerical solution U/t4 L82
M. Capello et al. PRL 2005
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A long range Jastrow correlation
can drive a metallic Fermi sea to a Mott
insulator!!
For an insulator

No charge stiffness
Incompressible fluid
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What in higher dimension?
Brinkmann-Rice
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Infinite dimension (DMFT)
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Now we can do the same in 2D(obviously we
neglect AF as in DMFT or in BR)
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KT means Kosterlitz-Thouless transition point,
explained later
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A clear transition is found
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Feynmann never lies (assumed)
Excitation energy induced by where
is the exact ground state of a physical
Hamiltonian
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Now let us start from the insulator
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Mapping to a classical model
Quantum Classical
For large U/t we are in the very dilute regime
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Now ask how can we satisfy
No way out, for any insulator Ugtgtt (any D)
In 2D a singular v between holon and doblon
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Exact mapping to the 2D CG model
We can classify all 2D insulators in terms of
true 2D Mott Insulator (no broken
translation symmetry)
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A KT transition is found
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In the plasma phase , similar to Luttinger
liquid Fermi surface but no Fermi
jump
Similar conclusions in Wen Bares PRB (1993)
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Instead in the confined phase
The density matrix appears to decay
exponentially i.e. the momentum distribution is
analytic in k
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Anomalous exponents for Z in 2D
t-J (projected wf) Hubbard
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From 2D Coulomb gas (see P. Minnhagen RPM 87)
The charge correlation decays as power law gt 4
because
A gap with power laws !!!
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It looks consistent, though it is impossible to
prove numerically
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New scenario T0 D2 (compatible with VMC on
Hubbard)
Fermi liquid Non Fermi liquid Mott Insulator
critical point
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Even more new scenario T0 D2 (long range
interactions?)
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• In the plasma phase for we
  have
• Z?0 Non Fermi liquid, singular at
• No d-wave ODLRO (preformed pairs at T0)
• pseudogap T0 phase (
  )

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Conclusions

• A Mott transition is found in 2D Hubbard (VMC)
• Mapping to 2D Coulomb gas
• confined phase Mott insulator
• plasma phaseNon Fermi liquid metal
• Critical Z?0 in the insulating/metallic phase
• Power law correlations in the insulator with gap

Non Fermi liquid phase possible in 2D?
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Finite doping ?