We investigate novel features of three-dimensional non-Hermitian Weyl semimetals,paying special attention to the unconventional bulk-boundary correspondence.We use the non-Bloch Chern numbers as the tool to obtain the...We investigate novel features of three-dimensional non-Hermitian Weyl semimetals,paying special attention to the unconventional bulk-boundary correspondence.We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram,which is also confirmed by the energy spectra from our numerical results.It is shown that,in sharp contrast to Hermitian systems,the conventional(Bloch)bulk-boundary correspondence breaks down in non-Hermitian topological semimetals,which is caused by the non-Hermitian skin effect.We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals:the topological edge modes are determined by the non-Bloch Chern number of the bulk bands.Moreover,these topological edge modes can manifest as the unidirectional edge motion,and their signatures are consistent with the non-Bloch bulk-boundary correspondence.Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.展开更多
In this study,we investigate the bulk-boundary and restricted phase space(RPS)thermodynamics of Rissner-Nordstrom(R-N)AdS and 6-dimensional charged Gauss-Bonnet AdS black holes.Additionally,we examine the topological ...In this study,we investigate the bulk-boundary and restricted phase space(RPS)thermodynamics of Rissner-Nordstrom(R-N)AdS and 6-dimensional charged Gauss-Bonnet AdS black holes.Additionally,we examine the topological characteristics of the considered black holes and compare them with the results of extended thermodynamics.We determine that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics,whereas the RPS thermodynamics exhibits a distinct behavior.Furthermore,we demonstrate that within the RPS formalism,there is only one critical point with a topological charge of+1(Q_(t)=+1).Moreover,in the RPS formalism,the inclusion of higher-derivative curvature terms in the form of GaussBonnet gravity does not alter the topological classification of critical points in charged AdS black holes.展开更多
We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials,and obtain phase diagrams regarding the presence and absence...We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials,and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes.The non-Hermitian skin effect(NHSE),which is known to break the bulk-boundary correspondence(BBC),emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder.The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart,whether with or without the NHSE.In one scenario without the NHSE,the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector.The NHSE itself also possesses some unusual behaviors in this system,including a high spectral winding without the presence of long-range hoppings,and a competition between two types of the NHSE,with the same and opposite inverse localization lengths for the two bands,respectively.Furthermore,it is found that the NHSE in this model does not always break the conventional BBC,which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.展开更多
We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by t...We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.It also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation.We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum.Furthermore,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum.In this way,the topological phases can be efficiently extracted through winding numbers.We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.展开更多
The bulk-boundary correspondence,which establishes the relationship between bulk topological invariants and the number of protected edge states,has been both theoretically and experimentally verified.However,some rece...The bulk-boundary correspondence,which establishes the relationship between bulk topological invariants and the number of protected edge states,has been both theoretically and experimentally verified.However,some recent theoretical studies have demonstrated the breakdown of bulk-boundary correspondence caused by specific symmetries where the entanglement spectrum,rather than the edge spectrum,could manifest the bulk topology more generally.Due to the difficulties in measuring this in physical systems,the bulk-entanglement spectrum correspondence has not yet been experimentally confirmed.Here,we report several one-dimensional and two-dimensional acoustic crystals in which we experimentally probe the nonlocal correlations with the fermion filling analog,thereby verifying the above correspondence.This work provides a useful platform to study the interplay among topological phases,symmetries,and the entanglement spectrum.展开更多
The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like...The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity.In this work,we discover a novel origin for pseudo-gaps when boundaries are introduced in a non-Hermitian lattice.It generically occurs due to the interference between two or more asymmetric pumping channels,and possess no analog in Hermitian systems.Mathematically,it can be visualized as being created by divergences of spectral flow in the complex energy plane,analogous to how sharp edges creates divergent electric fields near an electrical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary topological gaps,but the mid-gap modes are extended instead of edge-localized,and exhibit extreme sensitivity to symmetry-breaking perturbations.Surprisingly,pseudo-gaps can also host an integer number of edge modes even though the pseudo-bands possess fractional topological windings,or even no well-defined Chern number at all,in the marginal case of a phase transition point.Challenging conventional notions of topological bulk-boundary correspondences and even the very concept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as fractional Chern insulators.展开更多
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 ...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 comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra.Our design approach is based on a new electrostatics analogy for modifed non-Hermitian bulk-boundary correspondence,where electrostatic charge corresponds to density of states and electric felds correspond to complex spectral fow.As such,Hamiltonians of any desired spectra and state localization profle can be reverse-engineered,particularly those without any guiding symmetry principles.By recasting the diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem,our electrostatics analogy also transcends the gain/loss-induced compounding of foating-point errors in traditional numerical methods,thereby allowing access to far larger system sizes.展开更多
基金the National Natural Science Foundation of China(Grants No.11504143).
文摘We investigate novel features of three-dimensional non-Hermitian Weyl semimetals,paying special attention to the unconventional bulk-boundary correspondence.We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram,which is also confirmed by the energy spectra from our numerical results.It is shown that,in sharp contrast to Hermitian systems,the conventional(Bloch)bulk-boundary correspondence breaks down in non-Hermitian topological semimetals,which is caused by the non-Hermitian skin effect.We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals:the topological edge modes are determined by the non-Bloch Chern number of the bulk bands.Moreover,these topological edge modes can manifest as the unidirectional edge motion,and their signatures are consistent with the non-Bloch bulk-boundary correspondence.Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.
文摘In this study,we investigate the bulk-boundary and restricted phase space(RPS)thermodynamics of Rissner-Nordstrom(R-N)AdS and 6-dimensional charged Gauss-Bonnet AdS black holes.Additionally,we examine the topological characteristics of the considered black holes and compare them with the results of extended thermodynamics.We determine that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics,whereas the RPS thermodynamics exhibits a distinct behavior.Furthermore,we demonstrate that within the RPS formalism,there is only one critical point with a topological charge of+1(Q_(t)=+1).Moreover,in the RPS formalism,the inclusion of higher-derivative curvature terms in the form of GaussBonnet gravity does not alter the topological classification of critical points in charged AdS black holes.
文摘We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials,and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes.The non-Hermitian skin effect(NHSE),which is known to break the bulk-boundary correspondence(BBC),emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder.The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart,whether with or without the NHSE.In one scenario without the NHSE,the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector.The NHSE itself also possesses some unusual behaviors in this system,including a high spectral winding without the presence of long-range hoppings,and a competition between two types of the NHSE,with the same and opposite inverse localization lengths for the two bands,respectively.Furthermore,it is found that the NHSE in this model does not always break the conventional BBC,which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.
基金supported by the Natural Science Foundation of Zhejiang Province,China (Grant Nos.LR22A040001 and LY21A040004)the National Natural Science Foundation of China (Grant Nos.12074342 and 11835011)。
文摘We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.It also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation.We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum.Furthermore,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum.In this way,the topological phases can be efficiently extracted through winding numbers.We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.
基金supported by the National Natural Science Foundation of China(Grant No.12274219)the Key Research and Development Project of Jiangsu Province(Grant No.BE2022814).
文摘The bulk-boundary correspondence,which establishes the relationship between bulk topological invariants and the number of protected edge states,has been both theoretically and experimentally verified.However,some recent theoretical studies have demonstrated the breakdown of bulk-boundary correspondence caused by specific symmetries where the entanglement spectrum,rather than the edge spectrum,could manifest the bulk topology more generally.Due to the difficulties in measuring this in physical systems,the bulk-entanglement spectrum correspondence has not yet been experimentally confirmed.Here,we report several one-dimensional and two-dimensional acoustic crystals in which we experimentally probe the nonlocal correlations with the fermion filling analog,thereby verifying the above correspondence.This work provides a useful platform to study the interplay among topological phases,symmetries,and the entanglement spectrum.
基金funding support by the National Natural Science Foundation of China (12104519)the Guangdong Basic and Applied Basic Research Foundation (2020A1515110773)
文摘The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity.In this work,we discover a novel origin for pseudo-gaps when boundaries are introduced in a non-Hermitian lattice.It generically occurs due to the interference between two or more asymmetric pumping channels,and possess no analog in Hermitian systems.Mathematically,it can be visualized as being created by divergences of spectral flow in the complex energy plane,analogous to how sharp edges creates divergent electric fields near an electrical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary topological gaps,but the mid-gap modes are extended instead of edge-localized,and exhibit extreme sensitivity to symmetry-breaking perturbations.Surprisingly,pseudo-gaps can also host an integer number of edge modes even though the pseudo-bands possess fractional topological windings,or even no well-defined Chern number at all,in the marginal case of a phase transition point.Challenging conventional notions of topological bulk-boundary correspondences and even the very concept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as fractional Chern insulators.
基金supported by Singapore’s MOE Tier I grant WBS No.A-800022-00-00。
文摘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 comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra.Our design approach is based on a new electrostatics analogy for modifed non-Hermitian bulk-boundary correspondence,where electrostatic charge corresponds to density of states and electric felds correspond to complex spectral fow.As such,Hamiltonians of any desired spectra and state localization profle can be reverse-engineered,particularly those without any guiding symmetry principles.By recasting the diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem,our electrostatics analogy also transcends the gain/loss-induced compounding of foating-point errors in traditional numerical methods,thereby allowing access to far larger system sizes.
