Many-body approach to non-Hermitian physics in fermionic systems

In previous studies, the topological invariants of 1D non-Hermitian systems have been defined in open boundary condition (OBC) to satisfy the bulk-boundary correspondence. The extreme sensitivity of bulk energy spectra to boundary conditions has been attributed to the breakdown of the conventional bulk-boundary correspondence based on the topological invariants defined under periodic boundary condition (PBC). Here we propose non-Hermitian many-body polarization as a topological invariant for 1D non-Hermitian systems defined in PBC, which satisfies the bulk-boundary correspondence. Employing many-body methodology in the non-Hermitian Su-Schrieffer-Heeger model for fermions, we show the absence of non-Hermitian skin effect due to the Pauli exclusion principle and demonstrate the bulk-boundary correspondence using the invariant defined under PBC. Moreover, we show that the bulk topological invariant is quantized in the presence of chiral or generalized inversion symmetry. Our study suggests the existence of generalized crystalline symmetries in non-Hermitian systems, which give quantized topological invariants that capture the symmetry-protected topology of non-Hermitian systems.

[1]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[2]  Physical Review Letters 63 , 1989 .

[3]  R. Resta.  Theory of the electric polarization in crystals , 1992 .

[4]  Carmichael,et al.  Quantum trajectory theory for cascaded open systems. , 1993, Physical review letters.

[5]  Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum , 2001, math-ph/0110016.

[6]  A. Mostafazadeh.  Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian , 2001, math-ph/0107001.

[7]  A. Mostafazadeh.  Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries , 2002, math-ph/0203005.

[8]  장윤희,et al.  Y. , 2003, Industrial and Labor Relations Terms.

[9]  C. Bender.  Introduction to 𝒫𝒯-symmetric quantum theory , 2005, quant-ph/0501052.

[10]  Y. Hatsugai,et al.  Entanglement entropy and the Berry phase in the solid state , 2006, cond-mat/0601237.

[11]  Carl M. Bender,et al.  Making sense of non-Hermitian Hamiltonians , 2007, hep-th/0703096.

[12]  Z. Musslimani,et al.  Beam dynamics in PT symmetric optical lattices. , 2008, Physical review letters.

[13]  Shachar Klaiman,et al.  Visualization of branch points in PT-symmetric waveguides. , 2008, Physical review letters.

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

[15]  Ingrid Rotter,et al.  A non-Hermitian Hamilton operator and the physics of open quantum systems , 2009 .

[16]  M. Segev,et al.  Observation of parity–time symmetry in optics , 2010 .

[17]  L. Fidkowski.  Entanglement spectrum of topological insulators and superconductors. , 2009, Physical review letters.

[18]  P. Zoller,et al.  Topology by dissipation in atomic quantum wires , 2011, 1105.5947.

[19]  Hui Cao,et al.  Unidirectional invisibility induced by PT-symmetric periodic structures. , 2011, Physical review letters.

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

[21]  W. Marsden.  I and J , 2012 .

[22]  Li Ge,et al.  Pump-induced exceptional points in lasers. , 2011, Physical review letters.

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

[24]  Vilson R. Almeida,et al.  Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. , 2013, Nature materials.

[25]  M. Fleischhauer,et al.  Topological edge States in the one-dimensional superlattice Bose-Hubbard model. , 2013, Physical review letters.

[26]  T. Grover.  Entanglement of interacting fermions in quantum Monte Carlo calculations. , 2013, Physical review letters.

[27]  D. Christodoulides,et al.  Parity-time–symmetric microring lasers , 2014, Science.

[28]  Topological Photonics , 2014, 1408.6730.

[29]  Tony E. Lee,et al.  Heralded Magnetism in Non-Hermitian Atomic Systems , 2014, 1402.6700.

[30]  Shiyue Hua,et al.  Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators , 2014, Nature Photonics.

[31]  Tony E. Lee,et al.  Entanglement and spin squeezing in non-Hermitian phase transitions. , 2014, Physical review letters.

[32]  D. Brody.  Biorthogonal quantum mechanics , 2013, 1308.2609.

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

[34]  H. Yilmaz,et al.  Loss-induced suppression and revival of lasing , 2014, Science.

[35]  Hui Cao,et al.  Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics , 2015 .

[36]  C. Schneider,et al.  Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard , 2015, Nature.

[37]  Z. Q. Zhang,et al.  The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization , 2015, 1509.06886.

[38]  Andrea Alù,et al.  An invisible acoustic sensor based on parity-time symmetry , 2015, Nature Communications.

[39]  Congjun Wu,et al.  Detecting edge degeneracy in interacting topological insulators through entanglement entropy , 2014, 1405.2043.

[40]  Henning Schomerus,et al.  Topologically Protected Defect States in Open Photonic Systems with Non-Hermitian Charge-Conjugation and Parity-Time Symmetry. , 2015, Physical review letters.

[41]  Jianke Yang,et al.  Nonlinear waves in PT -symmetric systems , 2016, 1603.06826.

[42]  Luyao Jiang,et al.  Topological energy transfer in an optomechanical system with exceptional points , 2016, Nature.

[43]  P. Rabl,et al.  Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity , 2016, 1603.02325.

[44]  G. Weick,et al.  Topological collective plasmons in bipartite chains of metallic nanoparticles , 2016, 1611.03349.

[45]  Tony E. Lee,et al.  Anomalous Edge State in a Non-Hermitian Lattice. , 2016, Physical review letters.

[46]  Shinsei Ryu,et al.  Classification of topological quantum matter with symmetries , 2015, 1505.03535.

[47]  Y. Xiong.  Why does bulk boundary correspondence fail in some non-hermitian topological models , 2017, 1705.06039.

[48]  Masahito Ueda,et al.  Information Retrieval and Criticality in Parity-Time-Symmetric Systems. , 2017, Physical review letters.

[49]  Lan Yang,et al.  Exceptional points enhance sensing in an optical microcavity , 2017, Nature.

[50]  Y. Ashida,et al.  Parity-time-symmetric quantum critical phenomena , 2016, Nature Communications.

[51]  J. Bardarson,et al.  Bulk-boundary correspondence from the intercellular Zak phase , 2016, 1608.08232.

[52]  Stefano Longhi,et al.  Parity-time symmetry meets photonics: A new twist in non-Hermitian optics , 2017, 1802.05025.

[53]  Demetrios N. Christodoulides,et al.  Enhanced sensitivity at higher-order exceptional points , 2017, Nature.

[54]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[55]  J. E. Barrios Vargas,et al.  Topological states of non-Hermitian systems , 2018, The European Physical Journal Special Topics.

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

[57]  N. Kawakami,et al.  Non-Hermitian perspective of the band structure in heavy-fermion systems , 2018, Physical Review B.

[58]  Z. Q. Zhang,et al.  Experimental Demonstration of an Anisotropic Exceptional Point. , 2018, Physical review letters.

[59]  Zhong Wang,et al.  Edge States and Topological Invariants of Non-Hermitian Systems. , 2018, Physical review letters.

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

[61]  Demetrios N. Christodoulides,et al.  Non-Hermitian physics and PT symmetry , 2018, Nature Physics.

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

[63]  Y. Ashida,et al.  Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations. , 2017, Physical review letters.

[64]  F. Song,et al.  Non-Hermitian Chern Bands. , 2018, Physical review letters.

[65]  Liang Feng,et al.  Non-Hermitian photonics promises exceptional topology of light , 2018, Nature Communications.

[66]  Jan Carl Budich,et al.  Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems. , 2018, Physical review letters.

[67]  B. Gadway,et al.  Engineering tunable local loss in a synthetic lattice of momentum states , 2018, New Journal of Physics.

[68]  Aldenor G. Santos,et al.  Occurrence of the potent mutagens 2- nitrobenzanthrone and 3-nitrobenzanthrone in fine airborne particles , 2019, Scientific Reports.

[69]  W. Yi,et al.  Non-Bloch topological invariants in a non-Hermitian domain wall system , 2019, Physical Review B.

[70]  K. Imura,et al.  Generalized bulk-edge correspondence for non-Hermitian topological systems , 2019, Physical Review B.

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

[72]  Non-Hermitian Hopf-link exceptional line semimetals , 2018, Physical Review B.

[73]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[74]  Jiangbin Gong,et al.  Hybrid Higher-Order Skin-Topological Modes in Nonreciprocal Systems. , 2018, Physical review letters.

[75]  S. Longhi.  Probing non-Hermitian skin effect and non-Bloch phase transitions , 2019, Physical Review Research.

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

[77]  Flore K. Kunst,et al.  Non-Hermitian systems and topology: A transfer-matrix perspective , 2018, Physical Review B.

[78]  M. Soljačić,et al.  Topological photonics , 2014, Nature Photonics.

[79]  Flore K. Kunst,et al.  Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence , 2018, Physical Review B.

[80]  H. C. Wu,et al.  Inversion symmetric non-Hermitian Chern insulator , 2019, Physical Review B.

[81]  Ching Hua Lee,et al.  Anatomy of skin modes and topology in non-Hermitian systems , 2018, Physical Review B.

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

[83]  K. Moors,et al.  Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals , 2018, Physical Review B.

[84]  F. Song,et al.  Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems. , 2019, Physical review letters.

[85]  Z. Song,et al.  Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry , 2018, Physical Review B.

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

[87]  F. Song,et al.  Non-Hermitian Topological Invariants in Real Space. , 2019, Physical review letters.

[88]  S. Murakami,et al.  Non-Bloch Band Theory of Non-Hermitian Systems. , 2019, Physical review letters.

[89]  Hengyun Zhou,et al.  Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics. , 2019, Physical review letters.

[90]  Geometric characterization of non-Hermitian topological systems through the singularity ring in pseudospin vector space , 2019, Physical Review B.

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

[92]  N. Regnault,et al.  Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models , 2019, SciPost Physics.

[93]  K. Kawabata,et al.  Topological Origin of Non-Hermitian Skin Effects. , 2019, Physical review letters.

[94]  Dan S. Borgnia,et al.  Non-Hermitian Boundary Modes and Topology. , 2019, Physical review letters.

[95]  P. Alam.  ‘O’ , 2021, Composites Engineering: An A–Z Guide.

[96]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.