Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.

Journal of Physics Condensed MatterJul 20, 19981 citation

Dynamical properties of the S=12 random Heisenberg chain

Yu-Rong Shu, Maxime Dupont, Dao‐Xin Yao +2 more

We study dynamical properties at finite temperature $(T)$ of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor $S(q,\ensuremath{\omega})$ and its $\ensuremath{\omega}\ensuremath{\rightarrow}0$ limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate $1/{T}_{1})$ . Our study reveals a continuous narrow band of low-energy excitations in $S(q,\ensuremath{\omega})$, extending throughout the $q$ space, instead of being restricted to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as found in the uniform system. Close to $q=\ensuremath{\pi}$, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted $q$ dependence further away from $q=\ensuremath{\pi}$. Furthermore we also find spin diffusion effects close to $q=0$ that are not contained within the random-singlet theory but give non-negligible contributions to the mean $1/{T}_{1}$ . To compare with NMR experiments, we consider the distribution of the local relaxation rates $1/{T}_{1}$ . We show that the local $1/{T}_{1}$ values are broadly distributed, approximately according to a stretched exponential. The mean $1/{T}_{1}$ first decreases with $T$ , but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ${\ensuremath{\omega}}_{0}$. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean $1/{T}_{1}$ has never been experimentally observed. Indeed, we show that the divergence of the mean $1/{T}_{1}$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/{T}_{1}$ value is accessed.We study dynamical properties at finite temperature $(T)$ of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor $S(q,\ensuremath{\omega})$ and its $\ensuremath{\omega}\ensuremath{\rightarrow}0$ limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate $1/{T}_{1})$. Our study reveals a continuous narrow band of low-energy excitations in $S(q,\ensuremath{\omega})$, extending throughout the $q$ space, instead of being restricted to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as found in the uniform system. Close to $q=\ensuremath{\pi}$, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted $q$ dependence further away from $q=\ensuremath{\pi}$. Furthermore we also find spin diffusion effects close to $q=0$ that are not contained within the random-singlet theory but give non-negligible contributions to the mean $1/{T}_{1}$. To compare with NMR experiments, we consider the distribution of the local relaxation rates $1/{T}_{1}$. We show that the local $1/{T}_{1}$ values are broadly distributed, approximately according to a stretched exponential. The mean $1/{T}_{1}$ first decreases with $T$, but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ${\ensuremath{\omega}}_{0}$. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean $1/{T}_{1}$ has never been experimentally observed. Indeed, we show that the divergence of the mean $1/{T}_{1}$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/{T}_{1}$ value is accessed.

arXiv:1712.01701Physical review. B./Physical review. BMar 28, 201831 citations

Critical behavior of the S=3/2 Heisenberg chain

Adriana Moreo, K. Hallberg, Peter Horsch

APSMar 1, 19960 citations

We study dynamical properties at finite temperature

(T)

of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor $S(q,\ensuremath{\omega})$ and its $\ensuremath{\omega}\ensuremath{\rightarrow}0$ limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate

1/{T}_{1})

. Our study reveals a continuous narrow band of low-energy excitations in $S(q,\ensuremath{\omega})$, extending throughout the

q

space, instead of being restricted to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as found in the uniform system. Close to $q=\ensuremath{\pi}$, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted

q

dependence further away from $q=\ensuremath{\pi}$. Furthermore we also find spin diffusion effects close to

q=0

that are not contained within the random-singlet theory but give non-negligible contributions to the mean

1/{T}_{1}

. To compare with NMR experiments, we consider the distribution of the local relaxation rates

1/{T}_{1}

. We show that the local

1/{T}_{1}

values are broadly distributed, approximately according to a stretched exponential. The mean

1/{T}_{1}

first decreases with

T

, but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ${\ensuremath{\omega}}_{0}$. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean

1/{T}_{1}

has never been experimentally observed. Indeed, we show that the divergence of the mean

1/{T}_{1}

is due to rare events in the disordered chains and is concealed in experiments, where the typical

1/{T}_{1}

value is accessed.