Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States

Abstract

There are various research strategies used for non-Hermitian systems, which typically involve introducing non-Hermitian terms to pre-existing Hermitian Hamiltonians. It can be challenging to directly design non-Hermitian many-body models that exhibit unique features not found in Hermitian systems. In this Letter, we propose a new method to construct non-Hermitian many-body systems by generalizing the parent Hamiltonian method into non-Hermitian regimes. This allows us to build a local Hamiltonian using given matrix product states as its left and right ground states. We demonstrate this method by constructing a non-Hermitian spin-$1$ model from the asymmetric Affleck-Kennedy-Lieb-Tasaki (AKLT) state, which preserves both chiral order and symmetry-protected topological order. Our approach opens up a new paradigm for systematically constructing and studying non-Hermitian many-body systems, providing guiding principles to explore new properties and phenomena in non-Hermitian physics.

14 pages, 10 figures, to appear in Physical Review Letters

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-Hermitian Topology and Exceptional-Point Geometries
• Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
• String order and symmetries in quantum spin lattices
• Transient non-Hermitian skin effect
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Density matrix renormalization group approach for many-body open quantum systems
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins

Cited by in corpus (11)

• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces
• Many-body phase transitions in a non-Hermitian Ising chain
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Detecting Many-Body Scars from Fisher Zeros
• Composite Quantum Phases in Non-Hermitian Systems
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Quantifying non-Hermiticity using single- and many-particle quantum properties