Continuous phase transition without gap closing in non-Hermitian quantum many-body systems

Contrary to conventional wisdom in Hermitian systems, a continuous quantum phase transition between gapped phases is shown to occur without closing the gap ∆ in non-Hermitian quantum many-body systems. Here, the relevant length scale ξ ' vLR/∆ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i.e., unboundedness of vLR) rather than vanishing of the energy gap ∆. The susceptibility to a change in the system’s parameter exhibits a singularity due to nonorthogonality of eigenstates. As an illustrative example, we present an exactly solvable model by generalizing Kitaev’s toric-code model to non-Hermitian regimes.