Effects of interchain coupling on the thermodynamics of Kitaev ladder in a magnetic fields: Exact Diagonalization and Machine Learning Analysis

We investigate the thermodynamic behavior of the Kitaev ladder model under varying interchain coupling Kz and external magnetic fields using the finite-temperature Lanczos method and machinelearning approach. At zero magnetic field, we find that the specific heat exhibits a double-peak structure for finite Kz. The characteristic temperature TL of low-temperature peak increases significantly with increasing Kz, whereas the high-temperature peak remains insensitive to Kz. We argue that stronger interchain coupling elevates the characteristic temperature required for flux excitations. The further analysis to the specific-heat phase diagram under a magnetic field for different Kz values indicates that when the external magnetic field continuously increases, the specific heat of the system undergoes from well-defined two peaks to one peak, and the system finally enters a fully polarized phase. Concurrently, the low-temperature peak of the specific heat vanishes, which is corroborated in the thermodynamic limit predicted by machine-learning approach. As Kz decreases, weaker interchain coupling makes the system more susceptible to magnetization. These results demonstrate that the Kitaev ladder with finite Kz exhibits qualitatively similar character to the two-dimensional honeycomb Kitaev model under a magnetic field, highlighting the crucial role of interchain coupling in regulating flux excitation properties and stabilizing the spin liquid phase.