Matsumoto Norifumi, Kawabata Kohei, Ashida Yuto, Furukawa Shunsuke, Ueda Masahito
Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
Phys Rev Lett. 2020 Dec 31;125(26):260601. doi: 10.1103/PhysRevLett.125.260601.
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 Δ in non-Hermitian quantum many-body systems. Here, the relevant length scale ξ≃v_{LR}/Δ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i.e., unboundedness of v_{LR}) rather than vanishing of the energy gap Δ. 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.
与厄米系统中的传统观念相反，在非厄米量子多体系统中，能隙Δ不闭合时，带隙相之间会出现连续量子相变。在此，相关长度尺度ξ≃vLR/Δ发散，这是由于速度上的Lieb-Robinson界失效（即vLR无界），而非能隙Δ消失。由于本征态的非正交性，系统参数变化的磁化率呈现奇异性。作为一个示例，我们通过将Kitaev的环面码模型推广到非厄米区域，给出了一个精确可解模型。
