Mapping the Phase Diagram of the Interacting Kitaev Chain with Low-Temperature Chaos Diagnostics

The stability of Majorana qubits can be compromised by the onset of quantum chaos. While dynamical probes like the spectral form factor (SFF), out-of-time-ordered correlators (OTOCs), and the Loschmidt echo can detect chaos, spectral statistics via the mean level-spacing ratio (r̄) offer a concise metric for mapping chaotic parameter regimes. However, r̄ is an effectively infinite-temperature measure, poorly suited to probing the low-temperature regimes most relevant to qubit operation. In this work, we introduce a thermal mean level-spacing ratio, benchmarked against other well-known diagnostics, including SFF. We apply our diagnostic to the Sachdev-Ye-Kitaev (SYK) model to study its robustness as an indicator of chaos at low temperatures. For an interacting Kitaev chain, the thermal r̄ reveals many chaotic zones both within the topological phase and outside. This suggests fine-tuning of material properties could dramatically improve or compromise Majorana-qubit stability.