Phenomenology of Spectral Functions in Disordered Spin Chains at Infinite Temperature

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

Automated summary

Recent research on disordered spin chains has focused on the relationship between exact numerical calculations and the existence of a many-body localization phase transition, particularly in cases where disorder is significantly greater than spin interaction strength. A phenomenological theory based on proximity to the noninteracting limit, such as the Anderson insulator, has been introduced to explain intriguing features observed in these systems. This theory quantitatively describes the dynamics of certain observables in finite interacting systems across a wide range of disorders.