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arXiv:cond-mat/0308026 · Journal of Physics A Mathematical and General

Antiresonance and interaction-induced localization in spin and qubit chains with defects

M. I. Dykman, Léa Ferreira dos Santos

Published Oct 22, 2003• 13 citations
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Abstract

We study a spin chain with an anisotropic XXZ coupling in a magnetic field. Such a chain models several proposed types of quantum computers. The chain contains a defect with a different on-site energy. The interaction between excitations leads to the onset of two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive many-particle quantum interference eliminates this decay. Numerical results confirm the analytical predictions.

DOI
10.1088/0305-4470/36/44/l01

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We study a spin chain with an anisotropic XXZ coupling in a magnetic field. Such a chain models several proposed types of quantum computers. The chain contains a defect with a different on-site energy. The interaction between excitations leads to the onset of two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive many-particle quantum interference eliminates this decay. Numerical results confirm the analytical predictions.
We show that, in a system with defects, two-particle states may experience destructive quantum interference, or antiresonance. It prevents an excitation localized on a defect from decaying even where the decay is allowed by energy conservation. The system studied is a qubit chain or an equivalent spin chain with an anisotropic (XXZ)(\mathrm{XXZ})(XXZ) exchange coupling in a magnetic field. The chain has a defect with an excess on-site energy. It corresponds to a qubit with the level spacing different from other qubits. We show that, because of the interaction between excitations, a single defect may lead to multiple localized states. The energy spectra and localization lengths are found for two-excitation states. The localization of excitations facilitates the operation of a quantum computer. Analytical results for strongly anisotropic coupling are confirmed by numerical studies.
We analyze localization of interacting excitations in a system of qubits or spins. The system is modeled by a spin chain with an anisotropic (XXZ) exchange coupling in a magnetic field. Localization occurs on a defect with an excess on-site spin-flip energy. Such a defect corresponds to a qubit with the level spacing different from other qubits. Because of the interaction, a single defect may lead to multiple localized states. We find energy spectra and localization lengths of the two-excitation states. An excitation remains localized on the defect even where energy conservation allows scattering into extended states. This is due to destructive quantum interference in the two-excitation scattering channels, and it facilitates the operation of a quantum computer. Analytical results are obtained for strong anisotropy and are confirmed by numerical studies.
We study the dynamics of two types of pairs of excitations which are bound despite their strong repulsive interaction. One corresponds to doubly occupied sites in one-dimensional Bose–Hubbard systems, the so-called doublons. The other is pairs of neighboring excited spins in anisotropic Heisenberg spin-1/2 chains. We investigate the possibility of decay of the bound pairs due to resonant scattering by a defect or due to collisions of the pairs. We find that the amplitudes of the corresponding transitions are very small. This is the result of destructive quantum interference and explains the stability of the bound pairs.
We use a disordered antiferromagnetic spin-1∕21∕21∕2 chain with anisotropic exchange coupling to model an array of interacting qubits. All qubits have the same level spacing, except two, which are called the defects of the chain. The level spacings of the defects are equal and much larger than all the others. We investigate how the entanglement between the two defects depends on the anisotropy of the system. When the anisotropy coupling is much larger than the energy difference between a defect and an ordinary qubit, the two defects become strongly entangled. Small anisotropies, on the contrary, may decrease the entanglement, which is, in this case, also much affected by the number of excitations. The analysis is made for nearest-neighbor and next-nearest-neighbor defects. The decrease in the entanglement for nearest neighbor defects is not very significant, especially in large chains.
We investigate on how to generate maximally entangled states in systems characterized by the Hamiltonian of the XXZ\mathrm{XXZ}XXZ model with defects. Some proposed quantum computers are described by such a model. Defects embedded in this otherwise homogeneous spin chain are used to obtain Einstein-Podolsky-Rosen and W states. It is well known that a large defect localizes an excitation on the defect site. We can then consider a few identical and large defects to create a subsystem whose eigenstates are entangled. Here, we examine the cases of one and two excitations.
Many-particle confinement (localization) is studied for a 1D system of spinless fermions with nearest-neighbor hopping and interaction, or equivalently, for an anisotropic Heisenberg spin-1/2 chain. This system is frequently used to model quantum computers with perpetually coupled qubits. We construct a bounded sequence of site energies that leads to strong single-particle confinement of all states on individual sites. We show that this sequence also leads to a confinement of all many-particle states in an infinite system for a time that scales as a high power of the reciprocal hopping integral. The confinement is achieved for strong interaction between the particles while keeping the overall bandwidth of site energies comparatively small. The results show viability of quantum computing with time-independent qubit coupling.