Boundary Conformal Field Theory

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Boundary Conformal Field Theory Nano-structures

• The Kondo problem
• Boundary critical phenomena boundary conformal
  field theory
• Cr trimers on a Au surface a non-Fermi liquid
  fixed point
• with Andreas Ludwig Kevin Ingersent

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The Kondo Problem
J renormalizes to ? at low energies
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-electrons on sites 2, 3, are free -residual
local interactions, not involving impurity are
simply expressed in terms of free electron
operators and are irrelevant -a Fermi Liquid
Fixed Point
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Continuum formulation
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Boundary Critical Phenomena Boundary CFT
Very generally, 1D Hamiltonians which are
massless/critical in the bulk with interactions
at the boundary renormalize to conformally
invariant boundary conditions
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(J. Cardy)
bulk exponent ?
r
exponent, ? depends on universality class Of
boundary
Boundary layer non-universal
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• for non-Fermi liquid boundary conditions,
• boundary exponents ?bulk exponents
• trivial free fermion bulk exponents
• turn into non-trivial boundary exponents
• due to impurity interactions

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Cr Trimers on Au (111) Surfacea non-Fermi
liquid fixed point
Au
Cr (S5/2)

• Cr atoms can be manipulated
• and tunnelling current measured using
• a Scanning Tunnelling Microscope
• T Jamneala et al. PRL 87, 256804 (2001)

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STM tip
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• 2 doublet (s1/2) groundstates
• with opposite helicity
• ?gt?exp?i2?/3?gt under Si?Si1
• represent by s1/2 spin operators Saimp
• and p1/2 pseudospin operators ?aimp
• 3 channels of conduction electrons
• couple to the trimer
• these can be written in a basis of
• Pseudo-spin eigenstates, p-1,0,1

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only essential relevant Kondo interaction
(pseudo-spin label)

• we have found exact conformally
• invariant boundary condition by our
• usual tricks
• conformal embedding
• fusion