Lieb-Robinson bounds with dependence on interaction strengths
arXiv:1002.4190 · doi:10.1103/PhysRevA.81.062107
Abstract
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found that the Lieb-Robinson speed is not always algebraic in the interaction strengths. We consider Hamiltonians with any finite number of bounded operators and also a certain class of unbounded operators. We obtain bounds and propagation speeds for quantum systems on lattices and also general graphs possessing a kind of homogeneity and isotropy. One area for which this formalism could be useful is the study of quantum phase transitions which occur when interactions strengths are varied.
19 pages, 1 figure, minor modifications
References in corpus (11)
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Quantum criticality
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Propagation of Correlations in Quantum Lattice Systems
- General entanglement scaling laws from time evolution
- Quantum Graphity: a model of emergent locality
- Supersonic quantum communication
- Lieb-Robinson bounds and the speed of light from topological order
- Lieb-Robinson bounds for commutator-bounded operators
- Locality of dynamics in general harmonic quantum systems
- Statistical Mechanics of Graphity Models
Cited by in corpus (15)
- Stability of Frustration-Free Hamiltonians
- Hamiltonian complexity
- Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
- Strictly linear light cones in long-range interacting systems of arbitrary dimensions
- The Lieb-Robinson light cone for power-law interactions
- Locality and digital quantum simulation of power-law interactions
- Phase diagram and quench dynamics of the Cluster-XY spin chain
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
- Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field
- Much Ado About Something: Why Lieb-Robinson bounds are useful
- Exponential bound on information spreading induced by quantum many-body dynamics with long-range interactions
- Lieb-Robinson bounds on -partite connected correlation functions
- Sudden switch of generalized Lieb-Robinson velocity in a transverse field Ising spin chain
- Harnessing spin-qubit decoherence to probe strongly-interacting quantum systems