# Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension

## TL;DR

This study uses large-scale simulations to analyze how the NMR relaxation rate varies with temperature and disorder in one-dimensional spin chains, revealing its ability to detect quantum phase transitions and characterize the TLL parameter.

## Contribution

It introduces a comprehensive numerical analysis of the NMR relaxation rate across the superfluid-Bose glass transition, linking it to disorder effects and the TLL parameter in 1D systems.

## Key findings

- $1/T_1$ detects the quantum phase transition.
- $1/T_1$ probes the TLL parameter $K$.
- Distribution analysis aids experimental interpretation.

## Abstract

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/T_1$ in random one-dimensional spin chains as function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/T_1$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function in order to extract the $1/T_1$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.