7,794 research outputs found
Spin-Charge Separation and the Pauli Electron
The separation between the spin and the charge converts the quantum
mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian
Georgi-Glashow model, notorious for its magnetic monopoles and confinement. The
independent spin and charge fluctuations both lead to the Faddeev model,
suggesting the existence of a deep duality structure and indicating that the
fundamental carriers of spin and charge are knotted solitons.Comment: 7 pages; v2: new results added, references update
Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
At strong magnetic fields double-layer two-dimensional-electron-gas systems
can form an unusual broken symmetry state with spontaneous inter-layer phase
coherence. In this paper we explore the rich variety of quantum and
finite-temperature phase transitions associated with this broken symmetry. We
describe the system using a pseudospin language in which the layer
degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With
this mapping the spontaneous symmetry breaking is equivalent to that of a spin
1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge.
In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs
can be neutral or carry charge e. We derive an effective low-energy action and
use it to discuss the charged and collective neutral excitations of the system.
We have obtained the parameters of the Landau-Ginzburg functional from
first-principles estimates and from finite-size exact diagonalization studies.
We use these results to estimate the dependence of the critical temperature for
the Kosterlitz-Thouless phase transition on layer separation.Comment: 56 pages, 19 figures available upon request at
[email protected]. RevTex 3.0. IUCM94-00
Short-ranged RVB physics, quantum dimer models and Ising gauge theories
Quantum dimer models are believed to capture the essential physics of
antiferromagnetic phases dominated by short-ranged valence bond configurations.
We show that these models arise as particular limits of Ising (Z_2) gauge
theories, but that in these limits the system develops a larger local U(1)
invariance that has different consequences on different lattices. Conversely,
we note that the standard Z_2 gauge theory is a generalised quantum dimer
model, in which the particular relaxation of the hardcore constraint for the
dimers breaks the U(1) down to Z_2. These mappings indicate that at least one
realization of the Senthil-Fisher proposal for fractionalization is exactly the
short ranged resonating valence bond (RVB) scenario of Anderson and of
Kivelson, Rokhsar and Sethna. They also suggest that other realizations will
require the identification of a local low energy, Ising link variable {\it and}
a natural constraint. We also discuss the notion of topological order in Z_2
gauge theories and its connection to earlier ideas in RVB theory. We note that
this notion is not central to the experiment proposed by Senthil and Fisher to
detect vortices in the conjectured Z_2 gauge field.Comment: 17 pages, 4 postscript figures automatically include
Topological doping and the stability of stripe phases
We analyze the properties of a general Ginzburg-Landau free energy with
competing order parameters, long-range interactions, and global constraints
(e.g., a fixed value of a total ``charge'') to address the physics of stripe
phases in underdoped high-Tc and related materials. For a local free energy
limited to quadratic terms of the gradient expansion, only uniform or
phase-separated configurations are thermodynamically stable. ``Stripe'' or
other non-uniform phases can be stabilized by long-range forces, but can only
have non-topological (in-phase) domain walls where the components of the
antiferromagnetic order parameter never change sign, and the periods of charge
and spin density waves coincide. The antiphase domain walls observed
experimentally require physics on an intermediate lengthscale, and they are
absent from a model that involves only long-distance physics. Dense stripe
phases can be stable even in the absence of long-range forces, but domain walls
always attract at large distances, i.e., there is a ubiquitous tendency to
phase separation at small doping. The implications for the phase diagram of
underdoped cuprates are discussed.Comment: 18 two-column pages, 2 figures, revtex+eps
Mutual-Chern-Simons effective theory of doped antiferromagnets
A mutual-Chern-Simons Lagrangian is derived as a minimal field theory
description of the phase-string model for doped antiferromagnets. Such an
effective Lagrangian is shown to retain the full symmetries of parity,
time-reversal, and global SU(2) spin rotation, in contrast to conventional
Chern-Simons theories where first two symmetries are usually broken. Two
ordered phases, i.e., antiferromagnetic and superconducting states, are found
at low temperatures as characterized by dual Meissner effects and dual flux
quantization conditions due to the mutual-Chern-Simons gauge structure. A dual
confinement in charge/spin degrees of freedom occurs such that no true
spin-charge separation is present in these ordered phases, but the spin-charge
separation/deconfinement serves as a driving force in the unconventional phase
transitions of these ordered states to disordered states.Comment: 16 pages, 2 figures; published versio
A Model for Topological Fermions
We introduce a model designed to describe charged particles as stable
topological solitons of a field with values on the internal space S^3. These
solitons behave like particles with relativistic properties like Lorentz
contraction and velocity dependence of mass. This mass is defined by the energy
of the soliton. In this sense this model is a generalisation of the sine-Gordon
model from 1+1 dimensions to 3+1 dimensions, from S^1 to S^3. (We do not chase
the aim to give a four-dimensional generalisation of Coleman's isomorphism
between the Sine-Gordon model and the Thirring model which was shown in
2-dimensional space-time.) For large distances from the center of solitons this
model tends to a dual U(1)-theory with freely propagating electromagnetic
waves. Already at the classical level it describes important effects, which
usually have to be explained by quantum field theory, like
particle-antiparticle annihilation and the running of the coupling.Comment: 42 pages, 7 figures, more detailed calculations and comparison to
Skyrme model and 't Hooft-Polyakov monopoles adde
How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
Semiconducting nanowires in proximity to superconductors are promising
experimental systems for Majorana fermions, which may ultimately be used as
building blocks for topological quantum computers. A serious challenge in the
experimental realization of the Majorana fermions is the supression of
topological superconductivity by disorder. We show that Majorana fermions
protected by a robust topological gap can occur at the ends of a chain of
quantum dots connected by s-wave superconductors. In the appropriate parameter
regime, we establish that the quantum dot/superconductor system is equivalent
to a 1D Kitaev chain, which can be tuned to be in a robust topological phase
with Majorana end modes even in the case where the quantum dots and
superconductors are both strongly disordered. Such a spin-orbit coupled quantum
dot - s-wave superconductor array provides an ideal experimental platform for
the observation of non-Abelian Majorana modes.Comment: 8 pages; 3 figures; version 2: Supplementary material updated to
include more general proof for localized Majorana fermion
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