Light cone renormalization and quantum quenches in one-dimensional Hubbard models

Light cone renormalization and quantum quenches in one-dimensional Hubbard models

The Lieb–Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The ...

Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model.

We study the off-equilibrium dynamics of the infinite-dimensional Bose-Hubbard model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the ...

Renormalization of One-Dimensional Avalanche Models

We investigate a renormalization group (RG) scheme for avalanche automata introduced recently by Pietronero et al. to explain universality in self-organized criticality models. Using a modified approach, we construct exact RG equations Ibr a one-dimensional model whose detailed dynamics is exactly solvable. We then investigate in detail the effect of approximations inherent in a practical imple...

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

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Quantum phases of one-dimensional Hubbard models with three- and four-body couplings