Local spin dynamics near quantum critical line of spin-$1/2$ antiferromagnetic Heisenberg XXZ chain with longitudinal magnetic field

The spin-$1/2$ antiferromagnetic quantum XXZ chain is one of the most well-studied integrable model. Although all of its eigenstates and spectrum can be obtained via algebraic Bethe ansatz method, understanding its local dynamics remains a great challenge [1]. In the anisotropic gapped region, while tuning longitudinal field, there is a line of critical fields where the system undergoes quantum phase transitions. Recent experiments on $BaCo_{2}V_{2}O_{8}$ provided some evidences for understanding low-energy spin dynamics near critical line [2]. In this work, we further calculate local spin dynamics in this region in low frequency limit by form factor methods. Our results can be compared with measurements of NMR relaxation rate. [1] J.-S. Caux, H. Konno, M. Sorrell, and R. Weston, Journal of Statistical Mechanics: Theory and Experiment 2012, P01007 (2012) [2] S. Kimura, T. Takeuchi, K. Okunishi, M. Hagiwara, Z. He, K. Kindo, T. Taniyama, and M. Itoh, Physical review letters 100, 057202 (2008)