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

TL;DR

This paper demonstrates that in non-Hermitian quantum many-body systems, continuous phase transitions can occur without energy gap closing, driven by diverging length scales due to unbounded velocities, challenging traditional Hermitian system assumptions.

Contribution

It reveals a new mechanism for phase transitions in non-Hermitian systems where gap closing is not necessary, supported by an exactly solvable model.

Findings

Continuous phase transition without gap closing.

Divergence of length scale due to unbounded velocity.

Singular susceptibility from eigenstate nonorthogonality.

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