Localization and antiresonance in disordered qubit chains

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Localization and antiresonance in disordered
qubit chains
L. F. Santos
and M. I. Dykman Michigan State University
PRB 68, 214410 (03) JPA 36, L561 (03)

• Quantum computer modeled with an anisotropic
  spin-1/2 chain
• A defect in the chain a multiple localized
  many-excitation states
• Many particle antiresonance

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ONE EXCITATION
THE MODEL QCs with perpetually coupled
qubits Nuclear spins with dipolar
coupling Josephson junction systems Electrons on
helium
THE HAMILTONIAN
ELECTRONS
HELIUM
Energy
CONFINING ELECTRODES
Qubit energy difference can be controlled
Localized state on the defect no threshold in an
infinite chain. Localization length
g
e0
e0
e0
e0
n0
n02
n01
n0-1
Strong anisotropy Dgtgt1
study many-body effects in a disordered spin
system
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NON-RESONANT DEFECT g lt JD
RESONANT DEFECT g JD
TWO EXCITATIONS IDEAL CHAIN
ONE DEFECT AT n0
The bound pair NEXT to the defect becomes
strongly hybridized with the LDPs
Strong anisotropy Dgtgt1
Localized BOUND PAIRS one excitation on the
defect next to the defect (surface-type)
doublet
2e1gJD
Narrow band of bound pairs
bound pairs
localized BP
J/D
2e1JD
J/D
2e1JD
n0 1 n02
LDP

2J
2e1g
n0 n02
two magnons
Localized - delocalized pairs
Unbound magnons
Localization length
4J
2e1
2e1
4J
when JD g J/2
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SCATTERING PROBLEM FOR ANTIRESONANCE
TIME EVOLUTION (numerical results - 10 sites)
ANTIRESONANT DECOUPLING g JD
Resonanting bound pairs and states with one
excitation on the defect DO NOT mix
gJD/4
gJD
nonoverlapping bands, a pair NEXT to the defect
mixes with bound pairs only overlapping
bands a pair NEXT to the defect mixes with
localized-delocalized pairs only
The coefficient of reflection of the propagating
magnon from the defect R1
bound pair NEXT to the defect
Initial state
(n0 1, n0 2)

bound pair

n0
localized delocalized pair
Final state
(n0 2, n0 3)

(n0 , n0 3)
n0