5,965 research outputs found
Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
Investigations of emergent symmetry breaking phenomena occurring in small
finite-size systems are reviewed, with a focus on the strongly correlated
regime of electrons in two-dimensional semicoductor quantum dots and trapped
ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize
universal aspects and similarities of symmetry breaking found in these systems,
as well as in more traditional fields like nuclear physics and quantum
chemistry, which are characterized by very different interparticle forces. A
unified description of strongly correlated phenomena in finite systems of
repelling particles (whether fermions or bosons) is presented through the
development of a two-step method of symmetry breaking at the unrestricted
Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock
projection techniques. Quantitative and qualitative aspects of the two-step
method are treated and validated by exact diagonalization calculations.
Strongly-correlated phenomena emerging from symmetry breaking include: (I)
Chemical bonding, dissociation, and entanglement (at zero and finite magnetic
fields) in quantum dot molecules and in pinned electron molecular dimers formed
within a single anisotropic quantum dot. (II) Electron crystallization, with
particle localization on the vertices of concentric polygonal rings, and
formation of rotating electron molecules (REMs) in circular quantum dots. (III)
At high magnetic fields, the REMs are described by parameter-free analytic wave
functions, which are an alternative to the Laughlin and composite-fermion
approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating
traps and in analogy with the REMs, such repelling bosons form rotating boson
molecules (RBMs).Comment: Review article published in Reports on Progress in Physics. REVTEX4.
95 pages with 37 color figures. To download a copy with high-quality figures,
go to publication #82 in http://www.prism.gatech.edu/~ph274cy
Half moons are pinch points with dispersion
"Pinch points," singular features observed in (quasi-)elastic neutron
scattering, are a widely discussed hallmark of spin liquids with an emergent
gauge symmetry. Much less attention has been paid to "half moons," distinctive
crescent patterns at finite energy, which have been observed in experiments on
a number of pyrochlore magnets, and in a wide range of model calculations. Here
we unify these two phenomena within a single framework, paying particular
attention to the case of ordered, or field-saturated states, where pinch points
and half moons can be found in bands of excitations above a gap. We find that
half moons are nothing other than pinch points inscribed on a dispersing band.
Molecular dynamics simulations of the kagome lattice antiferromagnet are used
to explore how these bands evolve into the ground state and excitations of a
classical spin liquid. We explicitly demonstrate that this theory can reproduce
the pinch points and half moons observed in NdZrO.Comment: 6 pages, 4 figures. Supplementary material: 10 pages, 3 figure
Ising-nematic order in the bilinear-biquadratic model for the iron pnictides
Motivated by the recent inelastic neutron scattering (INS) measurements in
the iron pnictides which show a strong anisotropy of spin excitations in
directions perpendicular and parallel to the ordering wave-vector even above
the magnetic transition temperature , we study the frustrated Heisenberg
model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev
(DM) representation, which proves appropriate for all temperature regimes, we
find that the spin-spin dynamical structure factors are in excellent agreement
with experiment, exhibiting breaking of the symmetry even into the
paramagnetic region which we refer to as the Ising-nematic
phase. In addition to the Heisenberg spin interaction, we include the
biquadratic coupling and study its
effect on the dynamical temperature range of the Ising-nematic
phase. We find that this range reduces dramatically when even small values of
the interlayer exchange and biquadratic coupling are included. To
supplement our analysis, we benchmark the results obtained using the DM method
against those from different non-linear spin-wave theories, including the
recently developed generalized spin-wave theory (GSWT), and find good
qualitative agreement among the different theoretical approaches as well as
experiment for both the spin-wave dispersions and the dynamical structure
factors
Random Matrix Theories in Quantum Physics: Common Concepts
We review the development of random-matrix theory (RMT) during the last
decade. We emphasize both the theoretical aspects, and the application of the
theory to a number of fields. These comprise chaotic and disordered systems,
the localization problem, many-body quantum systems, the Calogero-Sutherland
model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions.
The review is preceded by a brief historical survey of the developments of RMT
and of localization theory since their inception. We emphasize the concepts
common to the above-mentioned fields as well as the great diversity of RMT. In
view of the universality of RMT, we suggest that the current development
signals the emergence of a new "statistical mechanics": Stochasticity and
general symmetry requirements lead to universal laws not based on dynamical
principles.Comment: 178 pages, Revtex, 45 figures, submitted to Physics Report
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