Bound state and Localization of excitation in many-body open systems

Abstract

Bound state and time evolution for single excitation in one dimensional XXZ spin chain within non-Markovian reservoir are studied exactly. As for bound state, a common feature is the localization of single excitation, which means the spontaneous emission of excitation into reservoir is prohibited. Exceptionally the pseudo-bound state can always be found, for which the single excitation has a finite probability emitted into reservoir. We argue that under limit $N\rightarrow \infty$ the pseudo-bound bound state characterizes an equilibrium between the localization in spin chain and spontaneous emission into reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists and it also is pseudo-bound state. The effect of quasirandom disorder is also discussed. It is found in this case that the single excitation is more inclined to locate at some spin sites. Thus a many-body-localization like behavior can be found. In order to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitation in spin chain studied exactly by numerically solving the evolution equation. A striking observation is that the excitation can be stayed at its initial location with a probability more than 0.9 when the bound state and disorder coexist. However if any one of the two issues is absent, the information of initial state can be erased completely or becomes mixed. Our finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.