Magnetic excitations in the one-dimensional Heisenberg–Ising model with external fields and their experimental realizations

Abstract

The one dimensional (1D) spin-1/2 Heisenberg-Ising model, a prototype quantum many-body system, has been intensively studied for many years. In this review, after a short introduction on some basic concepts of group theory for the octahedral group, a detailed pedagogical framework is laid down to derive the low-energy effective Hamiltonian for the Co-based materials. The 1D spin-1/2 Heisenberg-Ising model is obtained when applying the analysis to quasi-1D antiferromagnetic materials $\rm BaCo_2V_2O_8$ and $\rm SrCo_2V_2O_8$. After the preparation, we review the theoretical progresses of a variety of novel magnetic excitations and emergent physics in the 1D spin-1/2 Heisenberg-Ising model, and further summarize their recent experimental realizations.

K2RENb5O15 (RE = Ce, Pr, Nd, Sm, Gd–Ho): A Family of Quasi-One-Dimensional Spin-Chain Compounds with Large Interchain Distance

“…One-dimensional (1D) quantum spin chain (SC) materials, as an important paradigm of low-dimensional magnets, have attracted much attention as a platform to discover the exotic magnetic states predicted by theoretical models as well as the related quantum phenomena. − Compared to high-dimensional frustrated magnets, 1D interacting spin systems can host exotic magnetic ground states without geometric frustration owing to their intrinsic low dimensionality and low coordination number. In this system, a variety of nontrivial quantum phenomena, such as the Tomonaga–Luttinger (TL) liquid, , the ferrotoroidic order, Bose–Einstein condensation, and quantum criticality with emergent excitations, − have been theoretically proposed and experimentally reported. Also, a large variety of materials with a quasi-1D structural motif have been investigated, including the uniform and alternative linear SC, zigzag SC, spin ladder, and 1D spin tubes. ,− Among them, the S = 1/2 Heisenberg antiferromagnetic linear SC (AFMC) with only nearest-neighbor (NN) interactions has an exactly solvable ground state and which is a macroscopically entangled TL liquid state exhibiting topological spinon excitation. , To experimentally realize this exotic state, a large number of compounds, especially those containing 3d transition-metal (TM) ions, have been discovered and magnetically characterized in the past several decades. ,− While the real materials always undergo a three-dimensional (3D) long-range magnetic order due to the non-negligible interchain exchange interaction or structural distortion, the genuine 1D magnetic phase and related exotic magnetic phenomena remain not fully understood.…”