Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics.Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete s...Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics.Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices.The even-parity symmetries impose strict constraints on the scattering coefficients:the time-reversal(C and K) symmetries protect the symmetric transmission or reflection;the pseudo-Hermiticity(Q symmetry) or the inversion(P) symmetry protects the symmetric transmission and reflection.For the inversion-combined time-reversal symmetries,the symmetric features on the transmission and reflection interchange.The odd-parity symmetries including the particle-hole symmetry,chiral symmetry,and sublattice symmetry cannot ensure the scattering to be symmetric.These guiding principles are valid for both Hermitian and non-Hermitian linear systems.Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.展开更多
Knot theory provides a powerful tool for understanding topological matters in biology,chemistry,and physics.Here knot theory is introduced to describe topological phases in a quantum spin system.Exactly solvable model...Knot theory provides a powerful tool for understanding topological matters in biology,chemistry,and physics.Here knot theory is introduced to describe topological phases in a quantum spin system.Exactly solvable models with long-range interactions are investigated,and Majorana modes of the quantum spin system are mapped into different knots and links.The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers,which capture the geometric topologies of knots and links.The interactivity of energy bands is highlighted.In gapped phases,eigenstate curves are tangled and braided around each other,forming links.In gapless phases,the tangled eigenstate curves may form knots.Our findings provide an alternative understanding of phases in the quantum spin system,and provide insights into one-dimension topological phases of matter.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11975128 and 11874225).
文摘Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics.Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices.The even-parity symmetries impose strict constraints on the scattering coefficients:the time-reversal(C and K) symmetries protect the symmetric transmission or reflection;the pseudo-Hermiticity(Q symmetry) or the inversion(P) symmetry protects the symmetric transmission and reflection.For the inversion-combined time-reversal symmetries,the symmetric features on the transmission and reflection interchange.The odd-parity symmetries including the particle-hole symmetry,chiral symmetry,and sublattice symmetry cannot ensure the scattering to be symmetric.These guiding principles are valid for both Hermitian and non-Hermitian linear systems.Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.
基金Supported by the National Natural Science Foundation of China(Grants Nos.11874225,11975128,and 11605094)。
文摘Knot theory provides a powerful tool for understanding topological matters in biology,chemistry,and physics.Here knot theory is introduced to describe topological phases in a quantum spin system.Exactly solvable models with long-range interactions are investigated,and Majorana modes of the quantum spin system are mapped into different knots and links.The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers,which capture the geometric topologies of knots and links.The interactivity of energy bands is highlighted.In gapped phases,eigenstate curves are tangled and braided around each other,forming links.In gapless phases,the tangled eigenstate curves may form knots.Our findings provide an alternative understanding of phases in the quantum spin system,and provide insights into one-dimension topological phases of matter.
