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arXiv · 1912.09045

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

Norifumi Matsumoto·Kohei Kawabata·Yuto Ashida·Shunsuke Furukawa·Masahito Ueda
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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.

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Norifumi Matsumoto, Kohei Kawabata, Yuto Ashida, Shunsuke Furukawa, Masahito Ueda. 2019-12-19. Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems. https://doi.org/10.1103/physrevlett.125.260601

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