Magnetic excitations in the one-dimensional Heisenberg–Ising model with external fields and their experimental realizations
Jiahao Yang, Xiao Wang, Jianda Wu
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mtext>BaCo</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mn>8</mml:mn> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mtext>SrCo</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mn>8</mml:mn> </mml:msub> </mml:math> . 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.