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 $\Delta$ in non-Hermitian quantum many-body systems. Here, the relevant length scale $\xi \simeq v_{ \rm LR}/\Delta$ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i.e., unboundedness of $v_{ \rm LR}$) rather than vanishing of the energy gap $\Delta$. 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.
Categories: cond-mat.stat-mech cond-mat.str-el quant-ph