Lieb-Robinson bounds imply locality of interactions
arXiv:2006.10062 · doi:10.1103/PhysRevB.105.125101
Abstract
Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviours as well as fermionic lattice models. As a side-result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.
arXiv comment4.5 + 7 pages, 1 figure; v2: Changed title, added references, improved presentation
References in corpus (34)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- An Area Law for One Dimensional Quantum Systems
- Observation of entanglement propagation in a quantum many-body system
- Light-cone-like spreading of correlations in a quantum many-body system
- Non-local propagation of correlations in long-range interacting quantum systems
- Lieb-Schultz-Mattis in Higher Dimensions
- Spectral Gap and Exponential Decay of Correlations
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Spread of correlations in long-range interacting quantum systems
- Nearly-linear light cones in long-range interacting quantum systems
- Locality in Quantum and Markov Dynamics on Lattices and Networks
- Learning a local Hamiltonian from local measurements
- Breakdown of quasilocality in long-range quantum lattice models
- Index theory of one dimensional quantum walks and cellular automata
- Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
- Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
- A review of Quantum Cellular Automata
- Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
- Persistence of locality in systems with power-law interactions
- Finite speed of quantum scrambling with long range interactions
- Strictly linear light cones in long-range interacting systems of arbitrary dimensions
- Perturbative Gadgets at Arbitrary Orders
- Quantization of Hall Conductance For Interacting Electrons on a Torus
- Hierarchy of linear light cones with long-range interactions
- Hamiltonian Tomography via Quantum Quench
- A Multi-Dimensional Lieb-Schultz-Mattis Theorem
- Quasi-locality and efficient simulation of Markovian quantum dynamics
- An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
- Supersonic quantum communication
- Learning the dynamics of open quantum systems from their steady states
- Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
- Improving the Lieb-Robinson bound for long-range interactions
- On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems