Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet

TL;DR

This paper reveals a temperature-dependent crossover in the quantum Heisenberg spin chain, connecting low-temperature Tomonaga-Luttinger liquid behavior with high-temperature superdiffusive dynamics, supported by large-scale simulations.

Contribution

It demonstrates a spatiotemporal crossover between low- and high-temperature regimes in the quantum Heisenberg chain, unifying previously separate dynamical descriptions.

Findings

Superdiffusion onset scales with 1/T at longer length and timescales.

Crossover connects low-temperature Luttinger liquid and high-temperature superdiffusive regimes.

Experimental implications align with NMR measurements on Sr2CuO3.

Abstract

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-$1/2$ chain falls at low temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in $1+1$ dimensions. This Letter aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. As the temperature $T$ is reduced, we show that the onset of superdiffusion takes place at longer length and timescales $\propto 1/T$. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg $S=1/2$ chain compound Sr$_2$CuO$_3$, yet calls for new and dedicated experiments.