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Entanglement spectrum of a topological phase in one dimension
We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of…
Unbounded growth of entanglement in models of many-body localization.
The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state, which develops slowly over a diverging time scale as in glassy systems.
Many-body localization in a disordered quantum Ising chain.
Two entanglement properties that are promising for the study of the many-body localization transition are explored: the variance of the half-chainEntanglement entropy of exact eigenstates and the long time change in entanglements after a local quench from an specific eigenstate.
Symmetry protection of topological phases in one-dimensional quantum spin systems
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-S Haldane phase is a topologically nontrivial…
Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and…
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians
We show that the combination of charge and dipole conservation---characteristic of fracton systems---leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of…
One-dimensional symmetry protected topological phases and their transitions
We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this…
Detection of symmetry-protected topological phases in one dimension
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can be completely…
Time-evolving a matrix product state with long-ranged interactions
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one-dimensional…
Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians.
The quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder.