Hybrid critical line in the spin-1/2 XX chain with gamma interaction under transverse fields

We investigate the spin-1/2 XX chain with uniform Gamma interaction under a transverse magnetic field. By exactly diagonalizing the Hamiltonian using the Fermionization technique, we rigorously analyze the energy spectrum, distinguishing between gapped and gapless domains at absolute zero. Additionally, we thoroughly examine various order parameters, including magnetization, staggered magnetization, chirality, and spin nematicity, which delineate the diverse phases within the ground state phase diagram, each characterized by its unique long-range order. Notably, we identify a hybrid critical line in the ground state phase diagram. This hybrid critical line is defined as a line where multiple types of phase transitions converge. At points along this line, the system exhibits behaviors characteristic of different types of critical points simultaneously. Understanding the magnetic properties under different field conditions can lead to the development of new magnetic materials and technologies. Our results provide a framework for experimentally manipulating magnetic fields, allowing researchers to control and observe changes in material properties. This, in turn, offers valuable insights into the fundamental physics governing these systems.