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 $\mathrm{\Delta }$ in non-Hermitian quantum many-body systems. Here, the relevant length scale $\xi \simeq v_{\mathrm{LR}}/\mathrm{\Delta }$ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i.e., unboundedness of $v_{\mathrm{LR}}$) rather than vanishing of the energy gap $\mathrm{\Delta }$. 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.

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• Open quantum systems & decoherence
• Quantum phase transitions
• Topological phases of matter
• Lattice models in condensed matter