Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing.However,only non-Hermitian systems with real eigenenergies are stable,and great efforts have been devoted in designing them through enforcing parity-time(PT)symmetry.In this work,we exploit a lesser-known dynamical mechanism for enforcing real-spectra,and develop a comprehen-sive and versatile approach for designing new classes of parent Hamiltonians with real spectra.Our design approach is based on a new electrostatics analogy for modified non-Hermitian bulk-boundary cor-respondence,where electrostatic charge corresponds to density of states and electric fields correspond to complex spectral flow.As such,Hamiltonians of any desired spectra and state localization profile can be reverse-engineered,particularly those without any guiding symmetry principles.By recasting the diago-nalization of non-Hermitian Hamiltonians as a Poisson boundary value problem,our electrostatics anal-ogy also transcends the gain/loss-induced compounding of floating-point errors in traditional numerical methods,thereby allowing access to far larger system sizes.

Russell Yang;Jun Wei Tan;Tommy Tai;Jin Ming Koh;Linhu Li;Stefano Longhi;Ching Hua Lee

Department of Physics,National University of Singapore,Singapore 117551,Singapore;Clarendon Laboratory,University of Oxford,Oxford OX1 3PU,UK;Cavendish Laboratory,University of Cambridge,Cambridge CB3 OHE,UK;Division of Physics,Mathematics and Astronomy,Caltech,Pasadena,CA 91125,USA;Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing&School of Physics and Astronomy,Sun Yat-Sen University(Zhuhai Campus),Zhuhai 519082,China;Dipartimento di Fisica,Politecnico di Milano,Piazza Leonardo da Vinci 32,I-20133 Milan,Italy;IFISC(UIB-CSIC),Instituto de Fisica Interdisciplinary Sistemas Complejos,Palma de Mallorca E-07122,Spain

科学通报（英文版）

[1]Russell Yang;Jun Wei Tan;Tommy Tai;Jin Ming Koh;Linhu Li;Stefano Longhi;Ching Hua Lee-.Designing non-Hermitian real spectra through electrostatics)[J].科学通报（英文版）,2022(18):1865-1873

electrostatics,hermiticity,eigenenergies,Hamiltonians,respondence,recasting,diago,nalization

Designing,Hermitian,real,through,Non,presents,vast,newly,opened,territory,that,harbors,physics,applications,such,lasing,sensing,However,only,systems,stable,great,efforts,have,been,devoted,designing,them,enforcing,parity,PT,symmetry,In,this,work,exploit,lesser,known,dynamical,mechanism,develop,comprehen,sive,versatile,approach,classes,parent,Our,analogy,modified,bulk,boundary,where,charge,corresponds,density,states,electric,fields,complex,spectral,flow,any,desired,localization,profile,can,reverse,engineered,particularly,those,without,guiding,principles,By,Poisson,value,problem,our,also,transcends,gain,loss,induced,compounding,floating,point,errors,traditional,numerical,methods,thereby,allowing,access,far,larger,sizes

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