Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry

Abstract: The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. This work finds a continuous phase transition when disorder breaks permutation symmetry, with details of the transition being controlled by the degree of chaos in the clean limit. The system changes from an area law entangled phase in the permutation symmetric subspace where collective variables exist to volume law entanglement in the full Hilbert space, beyond a critical strength of the disorder. The critical strength tends to zero when the original disorder free system is fully chaotic. We study this mainly via the scaling of the collective spin of non-equilibrium states which transit to have properties of what has been dubbed "deep Hilbert space". This has potential implications for general many body physics, as well as technologies such as transmon qubits.