Symmetry-protected exceptional and nodal points in non-Hermitian systems

One of the unique features of non-Hermitian (NH) systems is the appearance of non-Hermitian degeneracies known as exceptional points (EPs). The occurrence of EPs in NH systems requires satisfying constraints whose number can be reduced in the presence of some symmetries. This results in stabilizing the appearance of EPs. Even though two different types of EPs, namely defective and non-defective EPs, may emerge in NH systems, exploring the possibilities of stabilizing EPs has been only addressed for defective EPs, at which the Hamiltonian becomes non-diagonalizable. In this letter, we show that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, may guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the non-Hermitian time-reversal symmetry in the two-band systems. We further show that the non-defective EPs manifest themselves by i) the diagonalizability of non-Hermitian Hamiltonian at these points and ii) the non-diagonalizability of the Hamiltonian along certain intersections of non-defective EPs. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary (Hermitian) nodal points may coexist with defective EPs in non-Hermitian models when the above symmetries are relaxed.

[1]  J. Wiersig.  Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems , 2022, Physical Review Research.

[2]  Wen-Jie Chen,et al.  Symmetry-protected topological exceptional chains in non-Hermitian crystals , 2022, Communications Physics.

[3]  Flore K. Kunst,et al.  Realizing exceptional points of any order in the presence of symmetry , 2022, Physical Review Research.

[4]  A. Dutt,et al.  Eigenvalue Topology of Non-Hermitian Band Structures in Two and Three Dimensions , 2021, 2022 Conference on Lasers and Electro-Optics (CLEO).

[5]  A. Grushin,et al.  Non-Hermitian chiral anomalies , 2021, Physical Review Research.

[6]  Shu Chen,et al.  Knot topology of exceptional point and non-Hermitian no-go theorem , 2021, 2111.11346.

[7]  Masatoshi Sato,et al.  Non-Hermitian higher-order Weyl semimetals , 2021, Physical Review B.

[8]  T. Hughes,et al.  Non-Hermitian higher-order Dirac semimetals , 2021, Physical Review B.

[9]  J. C. Budich,et al.  Fourth-order exceptional points in correlated quantum many-body systems , 2021, Physical Review B.

[10]  E. Bergholtz,et al.  Classification of exceptional nodal topologies protected by PT symmetry , 2021, Physical Review B.

[11]  Zhi Li,et al.  Homotopical characterization of non-Hermitian band structures , 2021 .

[12]  E. Bergholtz,et al.  Symmetry and Higher-Order Exceptional Points. , 2021, Physical review letters.

[13]  Y. Hatsugai,et al.  Symmetry-Protected Multifold Exceptional Points and Their Topological Characterization. , 2021, Physical review letters.

[14]  Jiangping Hu,et al.  Fermion Doubling Theorems in Two-Dimensional Non-Hermitian Systems for Fermi Points and Exceptional Points. , 2021, Physical review letters.

[15]  A. Grushin,et al.  Entanglement spectrum crossings reveal non-Hermitian dynamical topology , 2020, Physical Review Research.

[16]  E. Zhao,et al.  Knots and Non-Hermitian Bloch Bands. , 2020, Physical review letters.

[17]  Jan Carl Budich,et al.  Exceptional topology of non-Hermitian systems , 2019, 1912.10048.

[18]  Jiangping Hu,et al.  Jones Polynomial and Knot Transitions in Hermitian and non-Hermitian Topological Semimetals. , 2020, Physical review letters.

[19]  Qi Jie Wang,et al.  Electrically pumped topological laser with valley edge modes , 2020, Nature.

[20]  J. Ellis,et al.  PT -symmetric non-Hermitian quantum field theories with supersymmetry , 2020, Physical Review D.

[21]  Y. Chong,et al.  Non-Hermitian Dirac Cones. , 2019, Physical review letters.

[22]  S. Fan,et al.  Topological Classification of Non-Hermitian Hamiltonians , 2019, 1911.12748.

[23]  N. Kawakami,et al.  Chiral-symmetry protected exceptional torus in correlated nodal-line semimetals , 2019, Physical Review B.

[24]  E. Bergholtz,et al.  Hyperbolic nodal band structures and knot invariants , 2019, SciPost Physics.

[25]  F. Nori,et al.  Parity–time symmetry and exceptional points in photonics , 2019, Nature Materials.

[26]  K. Kawabata,et al.  Classification of Exceptional Points and Non-Hermitian Topological Semimetals. , 2019, Physical review letters.

[27]  Hengyun Zhou,et al.  Periodic table for topological bands with non-Hermitian symmetries , 2018, Physical Review B.

[28]  Masahito Ueda,et al.  Symmetry and Topology in Non-Hermitian Physics , 2018, Physical Review X.

[29]  E. Bergholtz,et al.  Knotted non-Hermitian metals , 2018, Physical Review B.

[30]  N. Kawakami,et al.  Symmetry-protected exceptional rings in two-dimensional correlated systems with chiral symmetry , 2018, Physical Review B.

[31]  B. Zhen,et al.  Exceptional surfaces in PT-symmetric non-Hermitian photonic systems , 2018, Optica.

[32]  T. Yokoyama,et al.  Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries , 2018, Physical Review B.

[33]  Flore K. Kunst,et al.  Symmetry-protected nodal phases in non-Hermitian systems , 2018, Physical Review B.

[34]  Kevin P. Chen,et al.  Experimental realization of a Weyl exceptional ring , 2018, Nature Photonics.

[35]  Ching Hua Lee,et al.  Tidal surface states as fingerprints of non-Hermitian nodal knot metals , 2018, Communications Physics.

[36]  E. Bergholtz,et al.  Exceptional links and twisted Fermi ribbons in non-Hermitian systems , 2018, Physical Review A.

[37]  M. Bandres,et al.  Topological insulator laser: Experiments , 2018, Science.

[38]  M. Bandres,et al.  Topological insulator laser: Theory , 2018, Science.

[39]  M. Bandres,et al.  Complex Edge-State Phase Transitions in 1D Topological Laser Arrays , 2017, 2018 Conference on Lasers and Electro-Optics (CLEO).

[40]  Y. Ashida,et al.  Topological Phases of Non-Hermitian Systems , 2018, Physical Review X.

[41]  M. Soljačić,et al.  Observation of bulk Fermi arc and polarization half charge from paired exceptional points , 2017, Science.

[42]  Liang Fu,et al.  Topological Band Theory for Non-Hermitian Hamiltonians. , 2017, Physical review letters.

[43]  Andrew K. Harter,et al.  Passive PT-symmetry breaking transitions without exceptional points in dissipative photonic systems , 2018 .

[44]  L. Fu,et al.  Non-Hermitian topological theory of finite-lifetime quasiparticles: Prediction of bulk Fermi arc due to exceptional point , 2017, Physical Review B.

[45]  M. Bandres,et al.  Towards the experimental realization of the topological insulator laser , 2017, 2017 Conference on Lasers and Electro-Optics (CLEO).

[46]  I. Sagnes,et al.  Lasing in topological edge states of a one-dimensional lattice , 2017, 1704.07310.

[47]  L. Duan,et al.  Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas. , 2016, Physical review letters.

[48]  Guo Chuan Thiang,et al.  Differential Topology of Semimetals , 2016, Communications in Mathematical Physics.

[49]  Ulrich Kuhl,et al.  Dynamically encircling an exceptional point for asymmetric mode switching , 2016, Nature.

[50]  M. Randeria,et al.  Are the surface Fermi arcs in Dirac semimetals topologically protected? , 2015, Proceedings of the National Academy of Sciences.

[51]  D. Christodoulides,et al.  Parity-time-symmetric coupled microring lasers operating around an exceptional point. , 2015, Optics letters.

[52]  Y. Wang,et al.  Single-mode laser by parity-time symmetry breaking , 2014, Science.

[53]  W. Heiss,et al.  The physics of exceptional points , 2012, 1210.7536.

[54]  U. Peschel,et al.  Parity–time synthetic photonic lattices , 2012, Nature.

[55]  M. Segev,et al.  PT-symmetry in honeycomb photonic lattices , 2011, 1103.3389.

[56]  R. Morandotti,et al.  Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.

[57]  C. Bender.  NON-HERMITIAN QUANTUM FIELD THEORY , 2005 .

[58]  M. Berry.  Physics of Nonhermitian Degeneracies , 2004 .

[59]  F. Keck,et al.  Unfolding a diabolic point: a generalized crossing scenario , 2003 .

[60]  Tosio Kato.  Perturbation theory in a finite-dimensional space , 1982 .