1. Michigan State University
Localization and antiresonance in disordered qubit chains
PRB 68, (03)
JPA 36, L561 (03)
L. F. Santos and M. I. Dykman
Michigan State University
Quantum computer modeled with an anisotropic spin-1/2 chain
A defect in the chain a multiple localized many-excitation states
Many particle antiresonance   
THE MODEL
QCs with perpetually coupled qubits:
Nuclear spins with dipolar coupling
Josephson junction systems
Electrons on helium
THE HAMILTONIAN
ONE EXCITATION e1
localized
excitation 2J
one magnon
e1 +(g2+J2)1/2
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
n0-1 n0
n0+1
n0+2
Strong anisotropy: D>>1
study many-body effects in a disordered spin system   
TWO EXCITATIONS: IDEAL CHAIN
NON-RESONANT DEFECT : g < JD
RESONANT DEFECT: g ~ JD
ONE DEFECT AT n0
The bound pair NEXT to the defect
becomes strongly hybridized with
the LDPs
Strong anisotropy
D>>1
Localized BOUND PAIRS:
one excitation on the defect
next to the defect (surface-type) 2J
J/D 4J
doublet
LDP
2e1+g+JD
2e1+JD
2e1+g
2e1 BP
doublet
2e1+g+JD
Narrow band of bound pairs
bound pairs
localized BP
n0 n0+1
2e1+JD
J/D
J/D
2e1+JD
n0 +1 n0+2
LDP + 2J
2e1+g
n0 +1 n0+2
n n0+2
two magnons
Localized - delocalized pairs
Unbound magnons
Localization length: 4J
2e1
2e1
n n 4J
when JD – g = J/2   
ANTIRESONANT DECOUPLING g ~ JD
SCATTERING PROBLEM
FOR ANTIRESONANCE
TIME EVOLUTION
(numerical results sites)
Resonanting bound pairs and states with
one excitation on the defect DO NOT mix
g=JD/4
g=JD
nonoverlapping bands,
a pair NEXT
to the defect mixes with
bound pairs only
overlapping bands:
localized-delocalized
pairs only
The coefficient of reflection of the propagating magnon
from the defect R=1
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