Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

Contrary to the conventional wisdom in Hermitian systems, a continuous quantum phase transition between gapped phases is shown to occur without closing the energy gap in non-Hermitian quantum many-body systems. Here, the relevant length scale v₋ₑ/ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i. e. , unboundedness of v₋ₑ) rather than vanishing of the energy gap. The susceptibility to a change in the system 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 a non-Hermitian regime.