1,113 research outputs found
Quantum Spin Formulation of the Principal Chiral Model
We formulate the two-dimensional principal chiral model as a quantum spin
model, replacing the classical fields by quantum operators acting in a Hilbert
space, and introducing an additional, Euclidean time dimension. Using coherent
state path integral techniques, we show that in the limit in which a large
representation is chosen for the operators, the low energy excitations of the
model describe a principal chiral model in three dimensions. By dimensional
reduction, the two-dimensional principal chiral model of classical fields is
recovered.Comment: 3pages, LATTICE9
Die Ad-hoc-Publizitätspflicht von Unternehmen nach amerikanischem Recht und die Auslegung von § 15 WpHG
Hofstadter butterfly as Quantum phase diagram
The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely
many phases, labelled by their (integer) Hall conductance, and a fractal
structure. We describe various properties of this phase diagram: We establish
Gibbs phase rules; count the number of components of each phase, and
characterize the set of multiple phase coexistence.Comment: 4 prl pages 1 colored figure typos corrected, reference [26] added,
"Ten Martini" assumption adde
Lehmann-Symanzik-Zimmermann Reduction Approach to Multi-Photon Scattering in Coupled-Resonator Arrays
We present a quantum field theoretical approach based on the
Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process
in a nano-architecture consisting of the coupled resonator arrays (CRA), which
are also coupled to some artificial atoms as the controlling quantum node. By
making use of this approach, we find the bound states of single photon for an
elementary unit, the T-type CRA, and explicitly obtain its multi-photon
scattering S-matrix in various situations. We also use this method to calculate
the multi-photon S-matrices for the more complex quantum network constructed
with main T-type CRA's, such as a H-type CRA waveguide.Comment: 15 pages, 14 figure
Chiral non-linear sigma-models as models for topological superconductivity
We study the mechanism of topological superconductivity in a hierarchical
chain of chiral non-linear sigma-models (models of current algebra) in one,
two, and three spatial dimensions. The models have roots in the 1D
Peierls-Frohlich model and illustrate how the 1D Frohlich's ideal conductivity
extends to a genuine superconductivity in dimensions higher than one. The
mechanism is based on the fact that a point-like topological soliton carries an
electric charge. We discuss a flux quantization mechanism and show that it is
essentially a generalization of the persistent current phenomenon, known in
quantum wires. We also discuss why the superconducting state is stable in the
presence of a weak disorder.Comment: 5 pages, revtex, no figure
Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
We study a quantum phase transition which occurs in a system composed of two
impurities (or quantum dots) each coupled to a different interacting
(Luttinger-liquid) lead. While the impurities are coupled electrostatically,
there is no tunneling between them. Using a mapping of this system onto a Kondo
model, we show analytically that the system undergoes a
Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the
Luttinger liquid parameter in the leads and the dot-lead interaction. The phase
with low values of the Luttinger-liquid parameter is characterized by an abrupt
switch of the population between the impurities as function of a common applied
gate voltage. However, this behavior is hard to verify numerically since one
would have to study extremely long systems. Interestingly though, at the
transition the entanglement entropy drops from a finite value of to
zero. The drop becomes sharp for infinite systems. One can employ finite size
scaling to extrapolate the transition point and the behavior in its vicinity
from the behavior of the entanglement entropy in moderate size samples. We
employ the density matrix renormalization group numerical procedure to
calculate the entanglement entropy of systems with lead lengths of up to 480
sites. Using finite size scaling we extract the transition value and show it to
be in good agreement with the analytical prediction.Comment: 12 pages, 9 figure
Tunneling and orthogonality catastrophe in the topological mechanism of superconductivity
We compute the angular dependence of the order parameter and tunneling
amplitude in a model exhibiting topological superconductivity and sketch its
derivation as a model of a doped Mott insulator. We show that ground states
differing by an odd number of particles are orthogonal and the order parameter
is in the d-representation, although the gap in the electronic spectrum has no
nodes. We also develop an operator algebra, that allowes one to compute
off-diagonal correlation functions.Comment: 4 pages, Revtex, psfig; some references are correcte
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