The infinite-temperature space- and time-dependent spin-correlation functions ${g}_{r}^{x}(t)$ are studied for the one-dimensional $\mathrm{XY}$ model. Numerical calculations are performed to obtain the exact autocorrelation function ${g}_{0}^{x}(t)$ for chains containing 5, 7, and 9 spins ( $S=\frac{1}{2}$ ). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that ${g}_{0}^{x}(t)$ for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that ${g}_{r}^{x}(t)$ for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for ${g}_{0}^{x}(t)$ is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.The infinite-temperature space- and time-dependent spin-correlation functions ${g}_{r}^{x}(t)$ are studied for the one-dimensional $\mathrm{XY}$ model. Numerical calculations are performed to obtain the exact autocorrelation function ${g}_{0}^{x}(t)$ for chains containing 5, 7, and 9 spins ($S=\frac{1}{2}$). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that ${g}_{0}^{x}(t)$ for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that ${g}_{r}^{x}(t)$ for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for ${g}_{0}^{x}(t)$ is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.

Physical review. B, Solid stateNov 1, 1975113 citations

Dynamical correlation functions of the XXZ spin- 1/2 chain

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

arXiv:hep-th/0407108Nuclear Physics BSep 17, 200583 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

Dynamical correlation functions for linear spin chains

Gerhard Müller, H. Beck

Physica B+CJan 1, 19771 citation

The infinite-temperature space- and time-dependent spin-correlation functions

{g}_{r}^{x}(t)

are studied for the one-dimensional

\mathrm{XY}

model. Numerical calculations are performed to obtain the exact autocorrelation function

{g}_{0}^{x}(t)

for chains containing 5, 7, and 9 spins (

S=\frac{1}{2}

). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that

{g}_{0}^{x}(t)

for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that

{g}_{r}^{x}(t)

for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for

{g}_{0}^{x}(t)

is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.

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.