Entanglement and the Sign Structure of Quantum States

Abstract

Many body quantum eigenstates of generic Hamiltonians at finite energy density typically satisfy "volume law" of entanglement entropy: the von Neumann entanglement entropy and the Renyi entropies for a subregion scale in proportion to its volume. Here we provide a connection between the volume law and the sign structure of eigenstates. In particular, we ask the question: can a positive wavefunction support a volume law entanglement? Remarkably, we find that a typical random positive wavefunction, exhibits a constant law for Renyi entanglement entropies $S_n$ for $n>1$, despite arbitrary large amplitude fluctuations. We also provide evidence that the modulus of the finite energy density eigenstates of generic local Hamiltonians show similar behavior.

6 pages, 3 figures

References in corpus (6)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Entanglement entropy of critical spin liquids
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems

Cited by in corpus (29)

• Quantum thermalization through entanglement in an isolated many-body system
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Integrating Neural Networks with a Quantum Simulator for State Reconstruction
• Renyi Entropy of Chaotic Eigenstates
• Neural Gutzwiller-projected variational wave functions
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
• A model for continuous thermal Metal to Insulator Transition
• Probing sign structure using measurement-induced entanglement
• Symmetry-protected sign problem and magic in quantum phases of matter
• Wavefunction positivization via automatic differentiation
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
• Bridging the gap between classical and quantum many-body information dynamics
• Holography and thermalization in optical pump-probe spectroscopy
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Highly entangled stationary states from strong symmetries
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• The Prime state and its quantum relatives
• Many-body quantum sign structures as non-glassy Ising models
• Sign problem in tensor network contraction
• Entanglement entropies and fermion signs of critical metals
• Entanglement transitions from restricted Boltzmann machines
• Achieving the volume-law entropy regime with random-sign Dicke states
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Dual-unitary shadow tomography
• Emergence of global receptive fields capturing multipartite quantum correlations
• Brute-force positivization of $J_1-J_2$ model ground states
• Principle of learning sign rules by neural networks in qubit lattice models