Dimensional reduction of Kitaev spin liquid at quantum criticality

We investigate the fate of the Kitaev spin liquid (KSL) under the influence of an external magnetic field $h$ in the [001] direction and upon tuning bond anisotropy of the Kitaev coupling $K_z$ keeping $K_x=K_y=K$. Guided by density matrix renormalization group, exact diagonalization, and with insights from parton mean field theory, we uncover a field-induced gapless-to-gapless Lifshitz transition from the nodal KSL to an intermediate gapless phase. The intermediate phase sandwiched between $h_{c1}$ and $h_{c2}$, which persists for a wide range of anisotropy $K_z\mathrm{/}K>0$, is composed of weakly coupled one-dimensional quantum critical chains. This intermediate phase is a dimensional crossover which asymptotically leads to the one-dimensional quantum Ising criticality characterized by the (1+1)D conformal field theory as the field reaches the phase transition at $h_{c2}$. Beyond $h_{c2}$ the system enters a partially polarized phase describable as effectively decoupled bosonic chains in which spin waves propagate along the one-dimensional zigzag direction. Our findings provide a comprehensive phase diagram and offer insights into the unusual physics of dimensional reduction generated by a uniform magnetic field in an otherwise two-dimensional quantum spin liquid.