Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method

Abstract

Efficient numerical methods are still lacking to probe the unconventional dynamics of quantum many-body systems under non-unitary evolution. In this work, we use Faber polynomials to numerically simulate both the dynamics of non-Hermitian systems and the quantum jumps unravelling of the Lindblad dynamics. We apply the method to the non-interacting and interacting Hatano-Nelson models evolving from two different setups: i) a Néel state, and ii) a domain wall. In the first case, we study how interactions preserve the initial magnetic order against the skin effect. In the second example, we present numerical evidence of the existence of an effective hydrodynamic description for the domain-wall melting problem in the non-interacting limit. Additionally, we investigate both the conditional and unconditional dynamics of the quantum jump unravelling in two quantum spin chains, which exhibit either the non-Hermitian or the Liouvillian skin effect. This numerical method inherently generalises the well-established method based on Chebyshev polynomials to accommodate non-Hermitian scenarios.

arXiv comment36 pages, 13 figures, Resubmission to SciPost, minor changes

References in corpus (86)

• Edge states and topological invariants of non-Hermitian systems
• Efficient simulation of one-dimensional quantum many-body systems
• Non-Hermitian Physics
• Entanglement entropy and conformal field theory
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Localization transitions in non-Hermitian quantum mechanics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependence of correlation functions following a quantum quench
• Calculation of reduced density matrices from correlation functions
• An Area Law for One Dimensional Quantum Systems
• Anomalous edge state in a non-Hermitian lattice
• The Kernel Polynomial Method
• The ITensor Software Library for Tensor Network Calculations
• Quantum trajectories and open many-body quantum systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Time-evolution methods for matrix-product states
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• A short introduction to the Lindblad Master Equation
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Non-reciprocal phase transitions
• Computational Studies of Quantum Spin Systems
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Non-Hermitian topological phenomena: A review
• Higher-order non-Hermitian skin effect
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Entanglement in a fermion chain under continuous monitoring
• Minimally Entangled Typical Thermal State Algorithms
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Finding Exponential Product Formulas of Higher Orders
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Measurement-induced quantum criticality under continuous monitoring
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Quantum Generalized Hydrodynamics
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• Skin effect and winding number in disordered non-Hermitian systems
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Chebyshev matrix product state approach for spectral functions
• Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects
• Superdiffusion in spin chains
• Critical delocalization of chiral zero energy modes in graphene
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• Spreading of correlations in Markovian open quantum systems
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Liouvillian Skin Effect in an Exactly Solvable Model
• KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures
• Spectral functions and time evolution from the Chebyshev recursion
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Anomalous Topological Active Matter
• Basis-Independent Spectral Methods for Non-linear Optical Response in Arbitrary Tight-binding Models
• A short introduction to Generalized Hydrodynamics
• Dissipative quasi-particle picture for quadratic Markovian open quantum systems
• Unusual wave-packet spreading and entanglement dynamics in non-Hermitian disordered many-body systems
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Numerical evaluation of Greens functions based on the Chebyshev expansion
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Hydrodynamical phase transition for domain-wall melting in the XY chain
• Dynamics of entanglement after exceptional quantum quench
• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps
• Chebyshev matrix product state approach for time evolution
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• Quenched dynamics in interacting one-dimensional systems: Appearance of current carrying steady states from initial domain wall density profiles
• Transport in one-dimensional integrable quantum systems
• Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media
• Density and current statistics in boundary-driven monitored fermionic chains
• Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect
• Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• From Bloch Oscillations to a Steady-State Current in Strongly Biased Mesoscopic Devices
• Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics
• Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device
• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
• Phase transitions of wave packet dynamics in disordered non-Hermitian systems
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Non-Hermitian and Liouvillian skin effects in magnetic systems

Cited by in corpus (10)

• Measurement-induced symmetry restoration and quantum Mpemba effect
• Entanglement Transition due to particle losses in a monitored fermionic chain
• Observables in non-Hermitian systems: A methodological comparison
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Exactly solvable models for universal operator growth
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
• Dissipative phase transition of interacting non-reciprocal fermions
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Entanglement Phase Transition in Chaotic non-Hermitian Systems