The real-time dynamics of equal-site correlation functions is studied for one-dimensional spin models with quenched disorder.Focusing on infinite temperature, we present a comparison between the dynamics of models with different quantum numbers S = 1 2 , 1, 3 2 , as well as of chains consisting of classical spins.Based on this comparison as well as by analyzing the statistics of energy-level spacings, we show that the putative many-body localization transition is shifted to considerably stronger values of disorder for increasing S. In this context, we introduce an effective disorder strength W eff , which provides a mapping between the dynamics for different spin quantum numbers.For small W eff , we show that the real-time correlations become essentially independent of S, and are moreover very well captured by the dynamics of classical spins.Especially for S = 3 2 , the agreement between quantum and classical dynamics is remarkably observed even for very strong values of disorder.This behavior also reflects itself in the corresponding spectral functions, which are obtained via a Fourier transform from the time to the frequency domain.As an aside, we also comment on the self-averaging properties of the correlation function at weak and strong disorder.Our work sheds light on the correspondence between quantum and classical dynamics at high temperatures and extends our understanding of the dynamics in disordered spin chains beyond the well-studied case of S = 1 2 .The real-time dynamics of equal-site correlation functions is studied for one-dimensional spin models with quenched disorder.Focusing on infinite temperature, we present a comparison between the dynamics of models with different quantum numbers S = 1 2 , 1, 3 2 , as well as of chains consisting of classical spins.Based on this comparison as well as by analyzing the statistics of energy-level spacings, we show that the putative many-body localization transition is shifted to considerably stronger values of disorder for increasing S. In this context, we introduce an effective disorder strength W eff , which provides a mapping between the dynamics for different spin quantum numbers.For small W eff , we show that the real-time correlations become essentially independent of S, and are moreover very well captured by the dynamics of classical spins.Especially for S = 3 2 , the agreement between quantum and classical dynamics is remarkably observed even for very strong values of disorder.This behavior also reflects itself in the corresponding spectral functions, which are obtained via a Fourier transform from the time to the frequency domain.As an aside, we also comment on the self-averaging properties of the correlation function at weak and strong disorder.Our work sheds light on the correspondence between quantum and classical dynamics at high temperatures and extends our understanding of the dynamics in disordered spin chains beyond the well-studied case of S = 1 2 .

arXiv:1911.09917Physical Review ResearchFeb 6, 202025 citations

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Eliott N. Rosenberg, Trond I. Andersen, Rhine Samajdar +97 more

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$ , of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.

arXiv:2306.09333Jun 15, 20234 citations

Quantum spin models at finite temperature

J. Oitmaa, Chris J. Hamer, Weihong Zheng

Cambridge University Press eBooksApr 6, 20060 citations

Dynamics of semi-infinite quantum spin chains atT=?

Joachim Stolze, V. S. Viswanath, Gerhard M�ller

The European Physical Journal BFeb 1, 199235 citations

P(\mathcal{M})

, of the magnetization transferred across the chain's center. The first two moments of

P(\mathcal{M})

show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.