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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
Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions
Non-local propagation of correlations in quantum systems with long-range interactions
TLDR
This work applies a variable-range Ising spin chain Hamiltonian and aVariable-range XY spin chainHamiltonian to a far-from-equilibrium quantum many-body system and observes its time evolution, determining the spatial and time-dependent correlations, extracting the shape of the light cone and measuring the velocity with which correlations propagate through the system.
Stability of Frustration-Free Hamiltonians
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call
Quantization of Hall Conductance for Interacting Electrons on a Torus
We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a
Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor
Elementary excitations in gapped quantum spin systems.
TLDR
It is shown that for translation invariant systems, simultaneous eigenstates of energy and momentum with an eigenvalue that is separated from the rest of the spectrum in that momentum sector can be arbitrarily well approximated by building a momentum superposition of a local operator acting on the ground state.
Stability of the Area Law for the Entropy of Entanglement
Recent results on the stability of the spectral gap under general perturbations for frustration-free Hamiltonians, have motivated the following question: Does the entanglement entropy of quantum
Non-local propagation of correlations in long-range interacting quantum systems
The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated [1–4] and how difficult the
Persistence of locality in systems with power-law interactions.
TLDR
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.
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