Rivero Jose D H, Ge Li
Department of Physics and Astronomy, College of Staten Island, CUNY, Staten Island, New York 10314, USA and The Graduate Center, CUNY, New York, New York 10016, USA.
Phys Rev Lett. 2020 Aug 21;125(8):083902. doi: 10.1103/PhysRevLett.125.083902.
Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this framework, a generalized symmetry that we term pseudochirality emerges naturally as the counterpart of symmetries defined by a commutation relation in quantum mechanics. Using this observation, we reveal previously unidentified constants of motion in non-Hermitian systems with parity-time and chiral symmetries. We further elaborate the disparate implications of pseudochirality induced constant of motion: It signals the pair excitation of a generalized "particle" and the corresponding "hole" but vanishes universally when the pseudochiral operator is antisymmetric. This disparity, when manifested in a non-Hermitian topological lattice with the Landau gauge, depends on whether the lattice size is even or odd. We further discuss previously unidentified symmetries of this non-Hermitian topological system, and we reveal how its constant of motion due to pseudochirality can be used as an indicator of whether a pure chiral edge state is excited.
诺特定理将运动常数与系统的对称性联系起来。在此，我们研究诺特定理在非厄米系统中的一种表现形式，其中内积的定义与量子力学不同。在这个框架中，一种我们称为赝手征性的广义对称性自然地作为量子力学中由对易关系定义的对称性的对应物出现。利用这一观察结果，我们揭示了具有宇称 - 时间和手征对称性的非厄米系统中先前未被识别的运动常数。我们进一步阐述了赝手征性诱导的运动常数的不同含义：它标志着广义“粒子”和相应“空穴”的对激发，但当赝手征算子反对称时普遍消失。这种差异在具有朗道规范的非厄米拓扑晶格中表现时，取决于晶格大小是偶数还是奇数。我们进一步讨论了这个非厄米拓扑系统先前未被识别的对称性，并揭示了由于赝手征性导致的其运动常数如何可以用作纯手征边缘态是否被激发的指标。
