964 research outputs found
Topological R\'enyi entropy after a quantum quench
We present an analytical study on the resilience of topological order after a
quantum quench. The system is initially prepared in the ground state of the
toric-code model, and then quenched by switching on an external magnetic field.
During the subsequent time evolution, the variation in topological order is
detected via the topological Renyi entropy of order 2. We consider two
different quenches: the first one has an exact solution, while the second one
requires perturbation theory. In both cases, we find that the long-term time
average of the topological Renyi entropy in the thermodynamic limit is the same
as its initial value. Based on our results, we argue that topological order is
resilient against a wide range of quenches.Comment: 5 pages, 4 figures, published version with structural changes, see
supplemental material at
http://link.aps.org/supplemental/10.1103/PhysRevLett.110.17060
Quantum geometric tensor away from Equilibrium
The manifold of ground states of a family of quantum Hamiltonians can be
endowed with a quantum geometric tensor whose singularities signal quantum
phase transitions and give a general way to define quantum phases. In this
paper, we show that the same information-theoretic and geometrical approach can
be used to describe the geometry of quantum states away from equilibrium. We
construct the quantum geometric tensor for ensembles of states
that evolve in time and study its phase diagram and equilibration properties.
If the initial ensemble is the manifold of ground states, we show that the
phase diagram is conserved, that the geometric tensor equilibrates after a
quantum quench, and that its time behavior is governed by out-of-time-order
commutators (OTOCs). We finally demonstrate our results in the exactly solvable
Cluster-XY model
Thermalization of Topological Entropy after a Quantum Quench
In two spatial dimensions, topological order is robust for static
deformations at zero temperature, while it is fragile at any finite
temperature. How robust is topological order after a quantum quench? In this
paper we show that topological order thermalizes under the unitary evolution
after a quantum quench. If the quench preserves gauge symmetry, there is a
residual topological entropy exactly like in the finite temperature case.
We obtain this result by studying the time evolution of the topological
2-R\'enyi entropy in a fully analytical, exact way. These techniques can be
then applied to systems with strong disorder to show whether a many-body
localization phenomenon appears in topologically ordered systems.Comment: new plot with finite time results added; typos fixe
Bipartite entanglement and entropic boundary law in lattice spin systems
We investigate bipartite entanglement in spin-1/2 systems on a generic
lattice. For states that are an equal superposition of elements of a group
of spin flips acting on the fully polarized state , we
find that the von Neumann entropy depends only on the boundary between the two
subsystems and . These states are stabilized by the group . A
physical realization of such states is given by the ground state manifold of
the Kitaev's model on a Riemann surface of genus . For a square
lattice, we find that the entropy of entanglement is bounded from above and
below by functions linear in the perimeter of the subsystem and is equal to
the perimeter (up to an additive constant) when is convex. The entropy of
entanglement is shown to be related to the topological order of this model.
Finally, we find that some of the ground states are absolutely entangled, i.e.,
no partition has zero entanglement. We also provide several examples for the
square lattice.Comment: 10 pages, figs, RevTeX
Probability density of quantum expectation values
We consider the quantum expectation value \mathcal{A}=\ of an
observable A over the state |\psi\> . We derive the exact probability
distribution of \mathcal{A} seen as a random variable when |\psi\> varies over
the set of all pure states equipped with the Haar-induced measure. The
probability density is obtained with elementary means by computing its
characteristic function, both for non-degenerate and degenerate observables. To
illustrate our results we compare the exact predictions for few concrete
examples with the concentration bounds obtained using Levy's lemma. Finally we
comment on the relevance of the central limit theorem and draw some results on
an alternative statistical mechanics based on the uniform measure on the energy
shell.Comment: Substantial revision. References adde
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