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

Abstract

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 $\xi \simeq v_{\mathrm{LR}}/\Delta$ 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 $\Delta$. 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.

7 + 5 pages, 1 + 2 figures