Locality of gapped ground states in systems with power-law decaying interactions
arXiv:2208.13057 · doi:10.1103/PRXQuantum.4.020348
Abstract
It has been proved that in gapped ground states of locally-interacting quantum systems, the effect of local perturbations decays exponentially with distance. However, in systems with power-law () decaying interactions, no analogous statement has been shown, and there are serious mathematical obstacles to proving it with existing methods. In this paper we prove that when exceeds the spatial dimension , the effect of local perturbations on local properties a distance away is upper bounded by a power law in gapped ground states, provided that the perturbations do not close the spectral gap. The power-law exponent is tight if and interactions are two-body, where we have . The proof is enabled by a method that avoids the use of quasiadiabatic continuation and incorporates techniques of complex analysis. This method also improves bounds on ground state correlation decay, even in short-range interacting systems. Our work generalizes the fundamental notion that local perturbations have local effects to power-law interacting systems, with broad implications for numerical simulations and experiments.
arXiv comment14 pages, 3 figures
References in corpus (43)
- Many-Body Physics with Ultracold Gases
- The density-matrix renormalization group in the age of matrix product states
- Quantum information with Rydberg atoms
- Probing many-body dynamics on a 51-atom quantum simulator
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
- Realizing a lattice spin model with polar molecules
- Bose-Einstein Condensation of Erbium
- Non-local propagation of correlations in long-range interacting quantum systems
- Lieb-Schultz-Mattis in Higher Dimensions
- Parallel implementation of high-fidelity multi-qubit gates with neutral atoms
- Spectral Gap and Exponential Decay of Correlations
- Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
- Topological quantum order: stability under local perturbations
- Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor
- Nearly-linear light cones in long-range interacting quantum systems
- A short proof of stability of topological order under local perturbations
- Stability of Frustration-Free Hamiltonians
- Breakdown of quasilocality in long-range quantum lattice models
- Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
- Finite speed of quantum scrambling with long range interactions
- Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems
- Probing site-resolved correlations in a spin system of ultracold molecules
- Strictly linear light cones in long-range interacting systems of arbitrary dimensions
- Quench Dynamics of a Fermi Gas with Strong Non-Local Interactions
- Hierarchy of linear light cones with long-range interactions
- The Lieb-Robinson light cone for power-law interactions
- Entanglement area laws for long-range interacting systems
- Locality and digital quantum simulation of power-law interactions
- An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
- Extending rotational coherence of interacting polar molecules in a spin-decoupled magic trap
- Information propagation for interacting particle systems
- Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
- Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
- Maximal speed for macroscopic particle transport in the Bose-Hubbard model
- Finite speed of quantum information in models of interacting bosons at finite density
- Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity
- Local Perturbations Perturb -Exponentially- Locally
- Bounding the finite-size error of quantum many-body dynamics simulations