We study the dynamics and thermodynamics of one-dimensional spin-orbital models relevant for transition-metal oxides. We show that collective spin, orbital, and combined spin-orbital excitations with infinite lifetime can exist, if the ground state of both sectors is ferromagnetic. Our main focus is the case of effectively ferromagnetic (antiferromagnetic) exchange for the spin (orbital) sector, and we investigate the renormalization of spin excitations via spin-orbital fluctuations using a boson-fermion representation. We contrast a mean-field decoupling approach with results obtained by treating the spin-orbital coupling perturbatively. Within the latter self-consistent approach we find a significant increase of the linewidth and additional structures in the dynamical spin structure factor as well as Kohn anomalies in the spin-wave dispersion caused by the scattering of spin excitations from orbital fluctuations. Finally, we analyze the specific heat $c(T)$ by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures $T$ we find numerically $c(T)~T$ pointing to a low-energy effective theory with dynamical critical exponent $z=1$ .We study the dynamics and thermodynamics of one-dimensional spin-orbital models relevant for transition-metal oxides. We show that collective spin, orbital, and combined spin-orbital excitations with infinite lifetime can exist, if the ground state of both sectors is ferromagnetic. Our main focus is the case of effectively ferromagnetic (antiferromagnetic) exchange for the spin (orbital) sector, and we investigate the renormalization of spin excitations via spin-orbital fluctuations using a boson-fermion representation. We contrast a mean-field decoupling approach with results obtained by treating the spin-orbital coupling perturbatively. Within the latter self-consistent approach we find a significant increase of the linewidth and additional structures in the dynamical spin structure factor as well as Kohn anomalies in the spin-wave dispersion caused by the scattering of spin excitations from orbital fluctuations. Finally, we analyze the specific heat $c(T)$ by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures $T$ we find numerically $c(T)~T$ pointing to a low-energy effective theory with dynamical critical exponent $z=1$.

arXiv:1101.5301Physical Review BJun 28, 201116 citations

Modified Spin-Wave Theory of Low-Dimensional Quantum Magnetic Systems

Ji-Hai Xu

Jan 1, 19930 citations

Dynamics of low energy wave packets in the one-dimensional quantum Heisenberg ferromagnet

Mateusz Kwaśnicki, Marcin Napiórkowski, Sören Petrat +1 more

Spin wave theory plays a central role in the analysis of low-energy properties of the quantum ferromagnetic Heisenberg model. In this work, we present a first step towards a rigorous justification of this approximation in the context of quantum dynamics in one dimension. According to spin wave theory, the evolution of a spin wave state should be well approximated by its free evolution with the appropriate energy of free quasiparticles called magnons. Our main result establishes this idea rigorously for a class of spin wave packets. We focus on spin- $\frac{1}{2}$ systems, and consider wave packets composed of two magnons. We argue our result is optimal with respect to the timescales.Spin wave theory plays a central role in the analysis of low-energy properties of the quantum ferromagnetic Heisenberg model. In this work, we present a first step towards a rigorous justification of this approximation in the context of quantum dynamics in one dimension. According to spin wave theory, the evolution of a spin wave state should be well approximated by its free evolution with the appropriate energy of free quasiparticles called magnons. Our main result establishes this idea rigorously for a class of spin wave packets. We focus on spin-$\frac{1}{2}$ systems, and consider wave packets composed of two magnons. We argue our result is optimal with respect to the timescales.

math-phCross-listedarXiv:2610.17883Oct 14, 20260 citations

Modified spin-wave study of random antiferromagnetic-ferromagnetic spin chains

Xin Wan, Kun Yang, R. N. Bhatt

We study the thermodynamics of a one-dimensional quantum spin-1/2 Heisenberg ferromagnetic system with random antiferromagnetic impurity bonds. In the dilute impurity limit, we generalize the modified spin-wave theory for random spin chains, where local chemical potentials for spin waves in ferromagnetic spin segments are introduced to ensure zero magnetization at finite temperature. This approach successfully describes the crossover from the behavior of a pure one-dimensional ferromagnet at high temperatures to a distinct Curie behavior due to randomness at low temperatures. We discuss the effects of impurity bond strength and concentration on the crossover and low-temperature behavior.We study the thermodynamics of a one-dimensional quantum spin-1/2 Heisenberg ferromagnetic system with random antiferromagnetic impurity bonds. In the dilute impurity limit, we generalize the modified spin-wave theory for random spin chains, where local chemical potentials for spin waves in ferromagnetic spin segments are introduced to ensure zero magnetization at finite temperature. This approach successfully describes the crossover from the behavior of a pure one-dimensional ferromagnet at high temperatures to a distinct Curie behavior due to randomness at low temperatures. We discuss the effects of impurity bond strength and concentration on the crossover and low-temperature behavior.

arXiv:cond-mat/0203326Physical review. B, Condensed matterJul 16, 20029 citations

Dynamics of thermal effects in the spin-wave theory of quantum antiferromagnets

Ángel Rivas, Miguel A. Martin-Delgado

arXiv:1112.3158Annals of PhysicsJan 2, 20135 citations

c(T)

by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures

T

we find numerically

c(T)~T

pointing to a low-energy effective theory with dynamical critical exponent

z=1

\frac{1}{2}

systems, and consider wave packets composed of two magnons. We argue our result is optimal with respect to the timescales.