16,968 research outputs found
GLC actors, artificial chemical connectomes, topological issues and knots
Based on graphic lambda calculus, we propose a program for a new model of
asynchronous distributed computing, inspired from Hewitt Actor Model, as well
as several investigation paths, concerning how one may graft lambda calculus
and knot diagrammatics
Tensor product representation of topological ordered phase: necessary symmetry conditions
The tensor product representation of quantum states leads to a promising
variational approach to study quantum phase and quantum phase transitions,
especially topological ordered phases which are impossible to handle with
conventional methods due to their long range entanglement. However, an
important issue arises when we use tensor product states (TPS) as variational
states to find the ground state of a Hamiltonian: can arbitrary variations in
the tensors that represent ground state of a Hamiltonian be induced by local
perturbations to the Hamiltonian? Starting from a tensor product state which is
the exact ground state of a Hamiltonian with topological order,
we show that, surprisingly, not all variations of the tensors correspond to the
variation of the ground state caused by local perturbations of the Hamiltonian.
Even in the absence of any symmetry requirement of the perturbed Hamiltonian,
one necessary condition for the variations of the tensors to be physical is
that they respect certain symmetry. We support this claim by
calculating explicitly the change in topological entanglement entropy with
different variations in the tensors. This finding will provide important
guidance to numerical variational study of topological phase and phase
transitions. It is also a crucial step in using TPS to study universal
properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure
Study of anyon condensation and topological phase transitions from a topological phase using Projected Entangled Pair States
We use Projected Entangled Pair States (PEPS) to study topological quantum
phase transitions. The local description of topological order in the PEPS
formalism allows us to set up order parameters which measure condensation and
deconfinement of anyons, and serve as a substitute for conventional order
parameters. We apply these order parameters, together with anyon-anyon
correlation functions and some further probes, to characterize topological
phases and phase transitions within a family of models based on a
symmetry, which contains quantum double, toric code, double
semion, and trivial phases. We find a diverse phase diagram which exhibits a
variety of different phase transitions of both first and second order which we
comprehensively characterize, including direct transitions between the toric
code and the double semion phase.Comment: 21+6 page
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