Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
arXiv:2307.03107 · doi:10.1103/PhysRevB.108.165114
Abstract
Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian systems, while the possible non-Hermitian solution remains outstanding. In this work, we generalize the quantum covariance matrix method to the cases that are applicable to non-Hermitian systems, through which we are able to explicitly reconstruct the non-Hermitian parent Hamiltonian from an arbitrary pair of biorthogonal eigenstates. As concrete examples, we successfully apply our approach in spin chain with Lee-Yang singularity and a non-Hermitian interacting fermion model. Some generalization and further application of our approach are also discussed. Our work provides a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates and shed light on future exploration on non-Hermitian physics.
arXiv comment8+4 pages, 3 figures
References in corpus (54)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Topological Photonics
- Quantum Simulation
- Non-Hermitian Physics
- Localization transitions in non-Hermitian quantum mechanics
- Quantum trajectories and open many-body quantum systems
- Biorthogonal Quantum Mechanics
- Non-Hermitian Many-Body Localization
- Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
- Experimental Quantum Hamiltonian Learning
- Projected Wavefunctions and High Temperature Superconductivity
- Learning a local Hamiltonian from local measurements
- Learning Quantum Systems
- Determining a local Hamiltonian from a single eigenstate
- Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
- Sample-efficient learning of quantum many-body systems
- Computational inverse method for constructing spaces of quantum models from wave functions
- Theoretical and Experimental Perspectives of Quantum Verification
- PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
- Hamiltonian Tomography via Quantum Quench
- Learning models of quantum systems from experiments
- Hamiltonian Learning for Quantum Error Correction
- Learning the dynamics of open quantum systems from their steady states
- Method to identify parent Hamiltonians for trial states
- Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
- Learning Quantum Hamiltonians from Single-qubit Measurements
- From Symmetries to Commutant Algebras in Standard Hamiltonians
- Entanglement guided search for parent Hamiltonians
- Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
- Construction of Hamiltonians by supervised learning of energy and entanglement spectra
- Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning
- Method for Estimating Spin-Spin Interactions from Magnetization Curves
- Entanglement Hamiltonian of Many-body Dynamics in Strongly-correlated Systems
- Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates
- Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model
- Numerical Methods for Detecting Symmetries and Commutant Algebras
- Search for exact local Hamiltonians for general fractional quantum Hall states
- From eigenstate to Hamiltonian: Prospects for ergodicity and localization
- Determining system Hamiltonian from eigenstate measurements without correlation functions
- Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
- Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
- Inverse Hamiltonian design by automatic differentiation
- Automatic design of Hamiltonians
- Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices
- High-accuracy Hamiltonian learning via delocalized quantum state evolutions
- Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
- Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
- Optimal parent Hamiltonians for time-dependent states
- Hamiltonian Assignment for Open Quantum Systems
- When can a local Hamiltonian be recovered from a steady state?
- Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient
- Composite Quantum Phases in Non-Hermitian Systems
- Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
- Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals