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

## TL;DR

This study uses density-matrix renormalization group methods to explore the phase diagram of the one-dimensional Kitaev model under a magnetic field, revealing emergent glassy behavior due to slow flux dynamics and local constraints.

## Contribution

It uncovers a novel emergent glass phase in a disorder-free Kitaev model, characterized by quasi-long-range correlations and multiple orthogonal flux configurations.

## Key findings

- Identified five distinct phases including an emergent glass phase.
- Confirmed glassiness through correlation functions and ground state fidelity.
- Attributed glassy behavior to slow Z2 flux dynamics caused by local constraints.

## Abstract

The complete phase diagram of the Kitaev model with a magnetic field remains elusive, as do the experimental results in the candidate material {\alpha}-RuCl3. 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 Z2 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 Z2 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.