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The Lieb-Robinson theorem states that the speed at which the correlations between two distant nodes in a spin network can be built through local interactions has an upper bound, which is called the Lieb-Robinson velocity. Our central aim is to demonstrate how to observe the Lieb-Robinson velocity in an Ising spin chain with a strong transverse field. We adopt and compare four correlation measures for characterizing different types of correlations, which include correlation function, mutual information, quantum discord, and entanglement of formation. We prove that one of correlation functions shows a special behavior depending on the parity of the spin number. All the information-theoretical correlation measures demonstrate the existence of the Lieb-Robinson velocity. In particular, we find that there is a sudden switch of the Lieb-Robinson speed with the increasing of the number of spin.
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian associated to the s
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
We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such
We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies itself a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a
Unitary dynamics with a strict causal cone (or light cone) have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory. Physical systems of