New Insights into the $J_1$-$J_2$ Spin Chain through Matrix Product States

Recent research has introduced a new approach to studying the $J_1$-$J_2$ spin-$1/2$ chain, utilizing a path integral framework based on matrix product states (MPS). This method captures the essential phases of the model, even at a semi-classical level, and aligns well with findings from field theory through abelian bosonization. The authors, F. Azad, Adam J. McRoberts, Chris Hooley, and A. G. Green, have demonstrated that the MPS framework not only provides a clear view of the dimerization transition but also facilitates a derivation of the critical phase's field theory. This derivation includes the correct topological term and an emergent $SO(4)$ symmetry, linking microscopic states to topological structures. The study highlights the relevance of an explicit dimerization potential, which plays a significant role in gapping out magnetic fluctuations. These findings could have implications for understanding quantum phase transitions and the behavior of strongly correlated electron systems. The full paper can be accessed at arXiv:2404.16088.