Time-polynomial Lieb-Robinson bounds for finite-range spin-network models

  title={Time-polynomial Lieb-Robinson bounds for finite-range spin-network models},
  author={Stefano Chessa and Vittorio Giovannetti},
  journal={Physical Review A},
The Lieb-Robinson bound sets a theoretical upper limit on the speed at which information can propagate in nonrelativistic quantum spin networks. In its original version, it results in an exponentially exploding function of the evolution time, which is partially mitigated by an exponentially decreasing term that instead depends upon the distance covered by the signal (the ratio between the two exponents effectively defining an upper bound on the propagation speed). In the present paper, by… 

Figures from this paper

Tightening the Lieb-Robinson Bound in Locally Interacting Systems

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays



Lieb-Robinson bounds and the generation of correlations and topological quantum order.

The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.

Lieb-Robinson bound at finite temperatures.

The Lieb-Robinson bound is extended to quantum systems at finite temperature by calculating the dynamical correlation function at nonzero temperature for systems whose interactions are, respectively, short range, exponentially decaying, and long range.

Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories.

It is argued that v_{B} is a state-dependent effective Lieb-Robinson velocity, which remains constant or decreases with decreasing temperature and is compared with free-particle computations to understand the role of strong coupling.

Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms

Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of nonrelativistic quantum lattice systems is essentially bounded. We review works

Lieb-Schultz-Mattis in higher dimensions

A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional spin systems is shown. The physical motivation for the result is that such spin systems typically either have long-range

Persistence of locality in systems with power-law interactions.

A new bound on the propagation of information in D-dimensional lattice models exhibiting 1/r^{α} interactions with α>D is derived, which qualitatively reproduce the short- and long-distance dynamical behavior following a local quench in an XY chain and a transverse-field Ising chain.

Topological quantum order: Stability under local perturbations

We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of

Correlation Decay in Fermionic Lattice Systems with Power-Law Interactions at Nonzero Temperature.

A bound on the correlation decay between anticommuting operators is proved and the bound is asymptotically tight, which is demonstrated by a high temperature expansion and by numerically analyzing density-density correlations in the one-dimensional quadratic Kitaev chain with long-range pairing.

Nearly linear light cones in long-range interacting quantum systems.

This work rules out the possibility that light cones of power-law interacting systems are bounded by a polynomial for α>2D and become linear as α→∞, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time.

Towards the fast scrambling conjecture

A bstractMany proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation times