相关论文: Locality in Quantum and Markov Dynamics on Lattice…

The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area…

We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of…

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…

Correlations and measures of entanglement in ground state wavefunctions of relativistic quantum field theories are spatially localized over length scales set by the mass of the lightest particle. We utilize this localization to design…

It has been proved that in gapped ground states of locally-interacting quantum systems, the effect of local perturbations decays exponentially with distance. However, in systems with power-law ($1/r^\alpha$) decaying interactions, no…

Non-positive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates…

Based on a result by Yarotsky (J. Stat. Phys. 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system…

We elaborate on the principle that for gapped quantum spin systems with local interaction "local perturbations [in the Hamiltonian] perturb locally [the ground state]". This principle was established in [Bachmann et al. 2012], relying on…

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the…

Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…

For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…

Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a…

Quantum correlations in a physical system are usually studied with respect to a unique (fixed) decomposition of the system into subsystems, without fully exploiting the rich structure of the state-space. Here, we show several examples in…

Using random matrices, we study the reduced dynamics of a two level system interacting with a generic environment. In the weak coupling limit, the result can be obtained directly from known results for purity decay, and result in Markovian…

Although entangled state vectors cannot be described in terms of classically realistic variables, localized in space and time, any given entanglement experiment can be built from basic quantum circuit components with well-defined locations.…

A Markov approximation in open quantum dynamics can give unphysical results when a map acts on a state that is not in its domain. This is examined here in a simple example, an open quantum dynamics for one qubit in a system of two…

We consider ground states in relatively bounded quantum perturbations of classical lattice models. We prove general results about such perturbations (existence of the spectral gap, exponential decay of truncated correlations, analyticity of…

We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property…

It is demonstrated here that local dynamics have the ability to strongly modify the entangling power of unitary quantum gates acting on a composite system. The scenario is common to numerous physical systems, in which the time evolution…

The effects of dynamic localization in a solid-state system -- a quantum dot -- are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent…