596 research outputs found
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
Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices
Hard constraints imposed in statistical mechanics models can lead to
interesting thermodynamical behaviors, but may at the same time raise
obstructions in the thoroughfare to thermal equilibration. Here we study a
variant of Baxter's 3-color model in which local interactions and defects are
included, and discuss its connection to triangular arrays of Josephson
junctions of superconductors and \textit{kagom\'e} networks of superconducting
wires. The model is equivalent to an Ising model in a hexagonal lattice with
the constraint that the magnetization of each hexagon is or 0. For
ferromagnetic interactions, we find that the system is critical for a range of
temperatures (critical line) that terminates when it undergoes an exotic first
order phase transition with a jump from a zero magnetization state into the
fully magnetized state at finite temperature. Dynamically, however, we find
that the system becomes frozen into domains. The domain walls are made of
perfectly straight segments, and domain growth appears frozen within the time
scales studied with Monte Carlo simulations. This dynamical obstruction has its
origin in the topology of the allowed reconfigurations in phase space, which
consist of updates of closed loops of spins. As a consequence of the dynamical
obstruction, there exists a dynamical temperature, lower than the (avoided)
static critical temperature, at which the system is seen to jump from a
``supercooled liquid'' to a ``polycrystalline'' phase. In contrast, for
antiferromagnetic interactions, we argue that the system orders for
infinitesimal coupling because of the constraint, and we observe no interesting
dynamical effects
Colored noise in the fractional Hall effect: duality relations and exact results
We study noise in the problem of tunneling between fractional quantum Hall
edge states within a four probe geometry. We explore the implications of the
strong-weak coupling duality symmetry existent in this problem for relating the
various density-density auto-correlations and cross-correlations between the
four terminals. We identify correlations that transform as either ``odd'' or
``anti-symmetric'', or ``even'' or ``symmetric'' quantities under duality. We
show that the low frequency noise is colored, and that the deviations from
white noise are exactly related to the differential conductance. We show
explicitly that the relationship between the slope of the low frequency noise
spectrum and the differential conductance follows from an identity that holds
to {\it all} orders in perturbation theory, supporting the results implied by
the duality symmetry. This generalizes the results of quantum supression of the
finite frequency noise spectrum to Luttinger liquids and fractional statistics
quasiparticles.Comment: 14 pages, 3 figure
Junctions of three quantum wires and the dissipative Hofstadter model
We study a junction of three quantum wires enclosing a magnetic flux. This is
the simplest problem of a quantum junction between Tomonaga-Luttinger liquids
in which Fermi statistics enter in a non-trivial way. We present a direct
connection between this problem and the dissipative Hofstadter problem, or
quantum Brownian motion in two dimensions in a periodic potential and an
external magnetic field, which in turn is connected to open string theory in a
background electromagnetic field. We find non-trivial fixed points
corresponding to a chiral conductance tensor leading to an asymmetric flow of
the current.Comment: 4 pages, 1 figur
Conformal quantum mechanics as the CFT dual to AdS
A 0+1-dimensional candidate theory for the CFT dual to AdS is
discussed. The quantum mechanical system does not have a ground state that is
invariant under the three generators of the conformal group. Nevertheless, we
show that there are operators in the theory that are not primary, but whose
"non-primary character" conspires with the "non-invariance of the vacuum" to
give precisely the correlation functions in a conformally invariant theory.Comment: 6 page
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