1,724 research outputs found
Dealing with a zombie in EU law: the regulatory procedure with scrutiny
Annotation to Joined Cases T-261/13 and T-86/14 Netherlands v. Commission, EU:T:2015:67
A quantum topological phase transition at the microscopic level
We study a quantum phase transition between a phase which is topologically
ordered and one which is not. We focus on a spin model, an extension of the
toric code, for which we obtain the exact ground state for all values of the
coupling constant that takes the system across the phase transition. We compute
the entanglement and the topological entropy of the system as a function of
this coupling constant, and show that the topological entropy remains constant
all the way up to the critical point, and jumps to zero beyond it. Despite the
jump in the topological entropy, the transition is second order as detected via
any local observable.Comment: (13 pages, 4 figures) v2: updated references and acknowledgments; v3:
final update (references) after publicatio
Exact results on the quench dynamics of the entanglement entropy in the toric code
We study quantum quenches in the two-dimensional Kitaev toric code model and
compute exactly the time-dependent entanglement entropy of the non-equilibrium
wave-function evolving from a paramagnetic initial state with the toric code
Hamiltonian. We find that the area law survives at all times. Adding disorder
to the toric code couplings makes the entanglement entropy per unit boundary
length saturate to disorder-independent values at long times and in the
thermodynamic limit. There are order-one corrections to the area law from the
corners in the subsystem boundary but the topological entropy remains zero at
all times. We argue that breaking the integrability with a small magnetic field
could change the area law to a volume scaling as expected of thermalized states
but is not sufficient for forming topological entanglement due to the presence
of an excess energy and a finite density of defects.Comment: 14 pages, 7 figures, published versio
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