Study on one-dimensional quantum spin systems by topological interaction and thermo quantum dynamics methods

Masuo Suzuki

Andrei A. Zvyagin

Mizuhiko Saeki

A form of the transverse magnetic susceptibility of a ferromagnetic spin system with a uniaxial anisotropy energy and an anisotropic exchange interaction, interacting with a phonon reservoir, is derived in the spin-wave approximation in terms of the non-equilibrium thermo-field dynamics (NETFD) using the TCLE method. The transverse magnetic susceptibility for the ferromagnetic system of one-dimensional infinite spins is studied by assuming a damped oscillator model of the phonon reservoir. The higher-order effects in the spin-wave approximation are numerically investigated. It is shown that the higher-order parts cannot be neglected for the spin system of the small magnitude and for the high temperature system, but may be neglected for the spin system of the large magnitude.

K. Katsumata

Ernest Teng Siang Ong

One dimensional quantum magnets have always been an active area of research due to their experimental realizability and the rich physics that they offer. By including geometrical frustration and additional interactions, it leads to even more novel and exotic quantum phases. In this thesis, we present the results of our investigations conducted by extending the quantum systems to spin–1. We conducted static, topological and dynamical calculations numerically on the spin–1 Heisenberg chain with Dzyaloshinskii–Moriya interaction in a uniform magnetic field in the form of a spin–1 Heisenberg chain in a helical magnetic field as well as the spin–1 Heisenberg model on the spin diamond and orthogonal dimer lattices. For the spin–1 Heisenberg chain in a helical field, we obtained the phase diagram using the density matrix renormalization group method and showed conclusively that the helical field destroys any topological order. We also obtained the dynamical spin structure factor spectra to study the magnon band structures and the softening of the modes near phase transitions. We then investigated the spin–1 Heisenberg model on the spin diamond and orthogonal dimer lattices using both exact diagonalization and the density matrix renormalization group method. We obtained the phase diagrams for both systems and explicitly calculated the magnetization, static spin structure and topological order of the different phases. Similar to the spin–1 Heisenberg chain in a helical magnetic field, we also obtained the dynamical spin structure factor spectra to study the characteristics of the lowest excitation occurring in both quantum systems.

Zhihuang Luo, Chao Lei, Jun Li +4 more

Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge, especially in interacting quantum system. Here we realize two to four spin one-dimensional Heisenberg chains using nuclear magnetic resonance simulators and observe interaction-induced topological transitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.