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The complete phase diagram of the Kitaev model with a magnetic field remainselusive, as do the experimental results in the candidate material{\alpha}-RuCl3. Here, we study the Kitaev model on a one-dimensional laddersetting within the density-matrix renormalization group method in the presenceof a magnetic field at zero temperature. We find five distinct phases withincreasing magnetic field, which are characterized by a homogeneous flux phase,the Z2 vortex gas, solid and emergent glass phase, and finally, aspin-polarized phase. The emergent glassiness is confirmed by calculatingcorrelation functions showing quasi-long-range behavior and ground statefidelity, showing a plethora of energetically accessible orthogonal saddlepoints corresponding to different flux configurations. This glassy behaviorseems to arise from the slow dynamics of the Z2 fluxes, which is a consequenceof the local constraints present in the underlying Hilbert space. Thisphenomenon can also be explored in other spin-liquid systems where thecorresponding low-energy excitations are similarly retarded due to constraints.

Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting