Impurity spin relaxation in S=1/2 XX chains

Abstract

Dynamic autocorrelations $<S_i^{\alpha }(t)S_i^{\alpha }>$ (α=x,z) of an isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin, defined by a local change in the nearest-neighbor coupling, is either in the bulk or at the boundary of the open-ended chain. The exact numerical calculation of the correlations employs the Jordan-Wigner mapping from spin operators to Fermi operators; effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior. At T=0 only power laws are present. At high T the x correlation decays exponentially (except at short times) while the z correlation still shows an asymptotic power law (different from the one at T=0) after an intermediate exponential phase. The boundary impurity correlations follow power laws at all T. The power laws for the z correlation and the boundary correlations can be deduced from the impurity-induced changes in the properties of the Jordan-Wigner fermion states.

Final version to be published in Phys. Rev. B. Three references added, extended discussion of relation to previous work

References in corpus (2)

• Temperature Correlations of Quantum Spins
• Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains

Cited by in corpus (10)

• Non-Markovian decay beyond the Fermi Golden Rule: Survival Collapse of the polarization in spin chains
• Boundary and impurity effects on entanglement of Heisenberg chains
• Diagonalization of quasi-uniform tridiagonal matrices
• Quantum state transfer in a XX chain with impurities
• On the effects of an impurity in an Ising-$XXZ$ diamond chain on the thermal entanglement, on the quantum coherence and on the quantum teleportation
• Dynamic structure factors of the spin-1/2 XX chain with Dzyaloshinskii-Moriya interaction
• Counting edge modes via dynamics of boundary spin impurities
• Effects of impurity on fidelity of quantum state transfer via spin channels
• Non-ergodic states induced by impurity levels in quantum spin chains
• Allosteric impurity effects in long spin chains