Emergent glassiness in the disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
K. B. Yogendra, Tanmoy Das, G. Baskaran
Abstract
The complete phase diagram of the Kitaev model with a magnetic field remains elusive, as do the experimental results in the candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. Here, we study the Kitaev model on a one-dimensional ladder setting within the density-matrix renormalization group method in the presence of a magnetic field at zero temperature. We find five distinct phases with increasing magnetic field, which are characterized by a homogeneous flux phase, the ${Z}_{2}$ vortex gas, solid and emergent glass phase, and finally, a spin-polarized phase. The emergent glassiness is confirmed by calculating correlation functions showing quasi-long-range behavior and ground state fidelity, showing a plethora of energetically accessible orthogonal saddle points corresponding to different flux configurations. This glassy behavior seems to arise from the slow dynamics of the ${Z}_{2}$ fluxes, which is a consequence of the local constraints present in the underlying Hilbert space. This phenomenon can also be explored in other spin-liquid systems where the corresponding low-energy excitations are similarly retarded due to constraints.