<p>The dichotomy of localization versus delocalization is a historic topic central to and widespread in quantum and condensed matter physics. Behind the complex scene, a few mechanisms are known to dominate the physics. Here, we show a delocalization mechanism attributed to a residue imaginary part of velocity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_2196_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\({{{\rm{Im}}}}(v)\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Im</mi> <mrow> <mo>(</mo> <mrow> <mi>v</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation>, feasible for ground states or low-temperature states of non-Hermitian quantum systems under periodic boundary conditions. In sharp contrast to conventional formalisms through extended wave functions, we discover that these target systems exhibit delocalization in collective physical properties such as correlation and entanglement of the Fermi Seas despite sometimes localized left and right single-particle eigenstates, as we demonstrate numerically and generalize to scenarios with finite temperatures and interaction. Disorder contributing to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_2196_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\({{{\rm{Im}}}}(v)\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Im</mi> <mrow> <mo>(</mo> <mrow> <mi>v</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> may also allow strong-disorder delocalization. Thus, the nontrivial physics of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_2196_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\({{{\rm{Im}}}}(v)\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Im</mi> <mrow> <mo>(</mo> <mrow> <mi>v</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> significantly enriches our understanding of and routes toward delocalization and harbors practical experiments and applications, such as in quantum transport and simulations.</p>

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Non-Hermitian delocalization induced by residue imaginary velocity

  • Shi-Xin Hu,
  • Yongxu Fu,
  • Yi Zhang

摘要

The dichotomy of localization versus delocalization is a historic topic central to and widespread in quantum and condensed matter physics. Behind the complex scene, a few mechanisms are known to dominate the physics. Here, we show a delocalization mechanism attributed to a residue imaginary part of velocity \({{{\rm{Im}}}}(v)\) Im ( v ) , feasible for ground states or low-temperature states of non-Hermitian quantum systems under periodic boundary conditions. In sharp contrast to conventional formalisms through extended wave functions, we discover that these target systems exhibit delocalization in collective physical properties such as correlation and entanglement of the Fermi Seas despite sometimes localized left and right single-particle eigenstates, as we demonstrate numerically and generalize to scenarios with finite temperatures and interaction. Disorder contributing to \({{{\rm{Im}}}}(v)\) Im ( v ) may also allow strong-disorder delocalization. Thus, the nontrivial physics of \({{{\rm{Im}}}}(v)\) Im ( v ) significantly enriches our understanding of and routes toward delocalization and harbors practical experiments and applications, such as in quantum transport and simulations.