Non-Hermitian Linear Response Theory

Abstract

Linear response theory lies at the heart of quantum many-body physics because it builds up connections between the dynamical response to an external probe and correlation functions at equilibrium. Here we consider the dynamical response of a Hermitian system to a non-Hermitian probe, and we develop a non-Hermitian linear response theory that can also relate this dynamical response to equilibrium properties. As an application of our theory, we consider the real-time dynamics of momentum distribution induced by one-body and two-body dissipations. We find that, for many cases, the dynamics of momentum occupation and the width of momentum distribution obey the same universal function, governed by the single-particle spectral function. We also find that, for critical state with no well-defined quasi-particles, the dynamics are slower than normal state and our theory provides a model independent way to extract the critical exponent. We apply our results to analyze recent experiment on the Bose-Hubbard model and find surprising good agreement between theory and experiment. We also propose to further verify our theory by carrying out a similar experiment on a one-dimensional Luttinger liquid.

6+3 pages, 3 figures; v2: supplementary material added

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• Non-Hermitian Topological Phases: Principles and Prospects
• Fundamental limits for reciprocal and non-reciprocal non-Hermitian quantum sensing
• Dimensional transmutation from non-Hermiticity
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems
• Non-Hermitian Squeezed Polarons
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• Theoretical Prediction of Non-Hermitian Skin Effect in Ultracold Atom Systems
• Emergent phase transition in Cluster Ising model with dissipation
• Kubo formula for non-Hermitian systems and tachyon optical conductivity
• Topological energy braiding of the non-Bloch bands
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Non-Hermitian Absorption Spectroscopy
• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Interaction induced dynamical $\mathcal{P}\mathcal{T}$ symmetry breaking in dissipative Fermi-Hubbard models
• Many-Body Open Quantum Systems
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Stability of Time-Reversal Symmetry Protected Topological Phases
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Dissipation-facilitated molecules in a Fermi gas with non-Hermitian spin-orbit coupling
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Response theory for nonequilibrium steady-states of open quantum systems
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
• Observation of universal dissipative dynamics in strongly correlated quantum gas
• Universal characteristics of one-dimensional non-Hermitian superconductors
• Page Curve from Non-Markovianity
• Exponentially Enhanced non-Hermitian Cooling
• Effective scattering and Efimov physics in the presence of two-body dissipation
• Measurements and analysis of response function of cold atoms in optical molasses
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• Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Multitude of exceptional points in van der Waals magnets
• Entropy Linear Response Theory with Non-Markovian Bath
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Fluctuation Response Patterns of Network Dynamics -- an Introduction
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Efimov physics in the complex plane
• Nonlinear Hall effects with an exceptional ring
• Dissipation induced transition between delocalization and localization in the three-dimensional Anderson model
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Computing n-time correlation functions without ancilla qubits
• Optomechanical Response of a Strongly Interacting Fermi Gas
• Nonadiabatic evolution and thermodynamics of a time-dependent open quantum system
• Dynamics of spatial phase coherence in a dissipative Bose-Hubbard atomic system
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• Fate of symmetry protected coherence in open quantum system
• Fermi polaron in a dissipative bath with spin-orbit coupling
• Quantum geometrical effects in non-Hermitian systems
• Fate of thermalization of ultracold fermions with two-body dissipation
• Dynamical Structure Factor from Weak Measurements
• Precision measurement for open systems by non-hermitian linear response
• Non-hermitian off-diagonal magnetic response of Dirac fermions
• Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes
• Quantum Point Contact with Local Two-body Loss
• Geometric Quantum Gates of Non-closed Paths Under Counterdiabatic Driving
• Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model
• Non-Hermitian Lindhard function and Friedel oscillations
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Physical constraints on effective non-Hermitian systems
• On the modeling of irreversibility by relaxator Liouville dynamics
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Precision-Induced Irreversibility in non-Hermitian systems
• Qudit-native measurement protocol for dynamical correlations using Hadamard tests
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Error bounds on the universal Lindblad equation in the thermodynamic limit