3,618 research outputs found
Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
In this work we present some new understanding of topological order,
including three main aspects: (1) It was believed that classifying topological
orders corresponds to classifying gapped quantum states. We show that such a
statement is not precise. We introduce the concept of \emph{gapped quantum
liquid} as a special kind of gapped quantum states that can "dissolve" any
product states on additional sites. Topologically ordered states actually
correspond to gapped quantum liquids with stable ground-state degeneracy.
Symmetry-breaking states for on-site symmetry are also gapped quantum liquids,
but with unstable ground-state degeneracy. (2) We point out that the
universality classes of generalized local unitary (gLU) transformations
(without any symmetry) contain both topologically ordered states and
symmetry-breaking states. This allows us to use a gLU invariant -- topological
entanglement entropy -- to probe the symmetry-breaking properties hidden in the
exact ground state of a finite system, which does not break any symmetry. This
method can probe symmetry- breaking orders even without knowing the symmetry
and the associated order parameters. (3) The universality classes of
topological orders and symmetry-breaking orders can be distinguished by
\emph{stochastic local (SL) transformations} (i.e.\ \emph{local invertible
transformations}): small SL transformations can convert the symmetry-breaking
classes to the trivial class of product states with finite probability of
success, while the topological-order classes are stable against any small SL
transformations, demonstrating a phenomenon of emergence of unitarity. This
allows us to give a new definition of long-range entanglement based on SL
transformations, under which only topologically ordered states are long-range
entangled.Comment: Revised version. Figures and references adde
Holographic Van der Waals phase transition for a hairy black hole
The Van der Waals(VdW) phase transition in a hairy black hole is investigated
by analogizing its charge, temperature, and entropy as the temperature,
pressure, and volume in the fluid respectively. The two point correlation
function(TCF), which is dual to the geodesic length, is employed to probe this
phase transition. We find the phase structure in the temperaturegeodesic
length plane resembles as that in the temperaturethermal entropy plane
besides the scale of the horizontal coordinate. In addition, we find the equal
area law(EAL) for the first order phase transition and critical exponent of the
heat capacity for the second order phase transition in the
temperaturegeodesic length plane are consistent with that in
temperaturethermal entropy plane, which implies that the TCF is a good probe
to probe the phase structure of the back hole.Comment: Accepted by Advances in High Energy Physics(The special issue:
Applications of the Holographic Duality to Strongly Coupled Quantum Systems
Holographic thermalization with a chemical potential in Gauss-Bonnet gravity
Holographic thermalization is studied in the framework of
Einstein-Maxwell-Gauss-Bonnet gravity. We use the two-point correlation
function and expectation value of Wilson loop, which are dual to the
renormalized geodesic length and minimal area surface in the bulk, to probe the
thermalization. The numeric result shows that larger the Gauss-Bonnet
coefficient is, shorter the thermalization time is, and larger the charge is,
longer the thermalization time is, which implies that the Gauss-Bonnet
coefficient can accelerate the thermalization while the charge has an opposite
effect. In addition, we obtain the functions with respect to the thermalization
time for both the thermalization probes at a fixed charge and Gauss-Bonnet
coefficient, and on the basis of these functions, we obtain the thermalization
velocity, which shows that the thermalization process is non-monotonic. At the
middle and later periods of the thermalization process, we find that there is a
phase transition point, which divides the thermalization into an acceleration
phase and a deceleration phase. We also study the effect of the charge and
Gauss-Bonnet coefficient on the phase transition point.Comment: 23 pages, many figures,footnote 4 is modified. arXiv admin note:
substantial text overlap with arXiv:1305.484
Holographic thermalization in noncommutative geometry
Gravitational collapse of a shell of dust in noncommutative geometry is
probed by the renormalized geodesic length, which is dual to probe the
thermalization by the two-point correlation function in the dual conformal
field theory. We find that larger the noncommutative parameter is, longer the
thermalization time is, which implies that the large noncommutative parameter
delays the thermalization process. We also investigate how the noncommutative
parameter affects the thermalization velocity and thermalization acceleration.Comment: some materials have been delete
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