73 research outputs found
The Energy Density in the Maxwell-Chern-Simons Theory
A two-dimensional nonrelativistic fermion system coupled to both
electromagnetic gauge fields and Chern-Simons gauge fields is analysed.
Polarization tensors relevant in the quantum Hall effect and anyon
superconductivity are obtained as simple closed integrals and are evaluated
numerically for all momenta and frequencies. The correction to the energy
density is evaluated in the random phase approximation (RPA), by summing an
infinite series of ring diagrams. It is found that the correction has
significant dependence on the particle number density.
In the context of anyon superconductivity, the energy density relative to the
mean field value is minimized at a hole concentration per lattice plaquette
(0.05 \sim 0.06) (p_c a/\hbar)^2 where p_c and a are the momentum cutoff and
lattice constant, respectively. At the minimum the correction is about -5 %
\sim -25 %, depending on the ratio (2m \omega_c)/(p_c^2) where \omega_c is the
frequency cutoff.
In the Jain-Fradkin-Lopez picture of the fractional quantum Hall effect the
RPA correction to the energy density is very large. It diverges logarithmically
as the cutoff is removed, implying that corrections beyond RPA become important
at large momentum and frequency.Comment: 19 pages (plain Tex), 12 figures not included, UMN-TH-1246/9
Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems
In this paper we reexamine the problem of the separation of spin and charge
degrees of freedom in two dimensional strongly correlated systems. We establish
a set of sufficient conditions for the occurence of spin and charge separation.
Specifically, we discuss this issue in the context of the Heisenberg model for
spin-1/2 on a square lattice with nearest () and next-nearest ()
neighbor antiferromagnetic couplings. Our formulation makes explicit the
existence of a local SU(2) gauge symmetry once the spin-1/2 operators are
replaced by bound states of spinons. The mean-field theory for the spinons is
solved numerically as a function of the ratio for the so-called s-RVB
Ansatz. A second order phase transition exists into a novel flux state for
. We identify the range as the s-RVB phase. It is characterized by the existence of a finite gap
to the elementary excitations (spinons) and the breakdown of all the continuous
gauge symmetries. An effective continuum theory for the spinons and the gauge
degrees of freedom is constructed just below the onset of the flux phase. We
argue that this effective theory is consistent with the deconfinement of the
spinons carrying the fundamental charge of the gauge group. We contrast this
result with the study of the one dimensional quantum antiferromagnet within the
same approach. We show that in the one dimensional model, the spinons of the
gauge picture are always confined and thus cannot be identified with the
gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.Comment: 56 pages, RevteX 3.
Chiral patterns arising from electrostatic growth models
Recently, unusual and strikingly beautiful seahorse-like growth patterns have
been observed under conditions of quasi-two-dimensional growth. These
`S'-shaped patterns strongly break two-dimensional inversion symmetry; however
such broken symmetry occurs only at the level of overall morphology, as the
clusters are formed from achiral molecules with an achiral unit cell. Here we
describe a mechanism which gives rise to chiral growth morphologies without
invoking microscopic chirality. This mechanism involves trapped electrostatic
charge on the growing cluster, and the enhancement of growth in regions of
large electric field. We illustrate the mechanism with a tree growth model,
with a continuum model for the motion of the one-dimensional boundary, and with
microscopic Monte Carlo simulations. Our most dramatic results are found using
the continuum model, which strongly exhibits spontaneous chiral symmetry
breaking, and in particular finned `S' shapes like those seen in the
experiments.Comment: RevTeX, 12 pages, 9 figure
W=0 pairing in Hubbard and related models of low-dimensional superconductors
Lattice Hamiltonians with on-site interaction have W=0 solutions, that
is, many-body {\em singlet} eigenstates without double occupation. In
particular, W=0 pairs give a clue to understand the pairing force in repulsive
Hubbard models. These eigenstates are found in systems with high enough
symmetry, like the square, hexagonal or triangular lattices. By a general
theorem, we propose a systematic way to construct all the W=0 pairs of a given
Hamiltonian. We also introduce a canonical transformation to calculate the
effective interaction between the particles of such pairs. In geometries
appropriate for the CuO planes of cuprate superconductors, armchair
Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound
state in a physically relevant range of parameters. We also show that W=0 pairs
quantize the magnetic flux like superconducting pairs do. The pairing mechanism
breaks down in the presence of strong distortions. The W=0 pairs are also the
building blocks for the antiferromagnetic ground state of the half-filled
Hubbard model at weak coupling. Our analytical results for the
Hubbard square lattice, compared to available numerical data, demonstrate that
the method, besides providing intuitive grasp on pairing, also has quantitative
predictive power. We also consider including phonon effects in this scenario.
Preliminary calculations with small clusters indicate that vector phonons
hinder pairing while half-breathing modes are synergic with the W=0 pairing
mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed
Matte
Chern_simons Theory of the Anisotropic Quantum Heisenberg Antiferromagnet on a Square Lattice
We consider the anisotropic quantum Heisenberg antiferromagnet (with
anisotropy ) on a square lattice using a Chern-Simons (or
Wigner-Jordan) approach. We show that the Average Field Approximation (AFA)
yields a phase diagram with two phases: a Ne{\`e}l state for
and a flux phase for separated by a
second order transition at . We show that this phase diagram does
not describe the regime of the antiferromagnet. Fluctuations around the
AFA induce relevant operators which yield the correct phase diagram. We find an
equivalence between the antiferromagnet and a relativistic field theory of two
self-interacting Dirac fermions coupled to a Chern-Simons gauge field. The
field theory has a phase diagram with the correct number of Goldstone modes in
each regime and a phase transition at a critical coupling . We identify this transition with the isotropic Heisenberg point. It
has a non-vanishing Ne{\` e}l order parameter, which drops to zero
discontinuously for .Comment: 53 pages, one figure available upon request, Revte
Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles
We give two formulations of exclusion statistics (ES) using a variable number
of bosonic or fermionic single-particle states which depend on the number of
particles in the system. Associated bosonic and fermionic ES parameters are
introduced and are discussed for FQHE quasiparticles, anyons in the lowest
Landau level and for the Calogero-Sutherland model. In the latter case, only
one family of solutions is emphasized to be sufficient to recover ES;
appropriate families are specified for a number of formulations of the
Calogero-Sutherland model. We extend the picture of variable number of
single-particle states to generalized ideal gases with statistical interaction
between particles of different momenta. Integral equations are derived which
determine the momentum distribution for single-particle states and distribution
of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE
The mechanism of spin and charge separation in one dimensional quantum antiferromagnets
We reconsider the problem of separation of spin and charge in one dimensional
quantum antiferromagnets. We show that spin and charge separation in one
dimensional strongly correlated systems cannot be described by the slave boson
or fermion representation within any perturbative treatment of the interactions
between the slave holons and slave spinons. The constraint of single occupancy
must be implemented exactly. As a result the slave fermions and bosons are not
part of the physical spectrum. Instead, the excitations which carry the
separate spin and charge quantum numbers are solitons. To prove this {\it
no-go} result, it is sufficient to study the pure spinon sector in the slave
boson representation. We start with a short-range RVB spin liquid mean-field
theory for the frustrated antiferromagnetic spin- chain. We derive
an effective theory for the fluctuations of the Affleck-Marston and Anderson
order parameters. We show how to recover the phase diagram as a function of the
frustration by treating the fluctuations non-perturbatively.Comment: 53 pages; Revtex 3.
Fractional Quantum Hall States of Clustered Composite Fermions
The energy spectra and wavefunctions of up to 14 interacting quasielectrons
(QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are
investigated using exact numerical diagonalization. It is shown that at
sufficiently high density the QE's form pairs or larger clusters. This
behavior, opposite to Laughlin correlations, invalidates the (sometimes
invoked) reapplication of the composite fermion picture to the individual QE's.
The series of finite-size incompressible ground states are identified at the QE
filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings
nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4,
1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states
were recently discovered experimentally. Detailed analysis indicates that QE or
QH correlations in these states are different from those of well-known FQH
electron states (e.g., Laughlin or Moore-Read states), leaving the origin of
their incompressibility uncertain. Halperin's idea of Laughlin states of QP
pairs is also explored, but is does not seem adequate.Comment: 14 pages, 9 figures; revision: 1 new figure, some new references,
some new data, title chang
Spin-Charge Separation in the Model: Magnetic and Transport Anomalies
A real spin-charge separation scheme is found based on a saddle-point state
of the model. In the one-dimensional (1D) case, such a saddle-point
reproduces the correct asymptotic correlations at the strong-coupling
fixed-point of the model. In the two-dimensional (2D) case, the transverse
gauge field confining spinon and holon is shown to be gapped at {\em finite
doping} so that a spin-charge deconfinement is obtained for its first time in
2D. The gap in the gauge fluctuation disappears at half-filling limit, where a
long-range antiferromagnetic order is recovered at zero temperature and spinons
become confined. The most interesting features of spin dynamics and transport
are exhibited at finite doping where exotic {\em residual} couplings between
spin and charge degrees of freedom lead to systematic anomalies with regard to
a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic
fluctuation with a small, doping-dependent energy scale is found, which is
characterized in momentum space by a Gaussian peak at (, ) with
a doping-dependent width (, is the doping
concentration). This commensurate magnetic fluctuation contributes a
non-Korringa behavior for the NMR spin-lattice relaxation rate. There also
exits a characteristic temperature scale below which a pseudogap behavior
appears in the spin dynamics. Furthermore, an incommensurate magnetic
fluctuation is also obtained at a {\em finite} energy regime. In transport, a
strong short-range phase interference leads to an effective holon Lagrangian
which can give rise to a series of interesting phenomena including linear-
resistivity and Hall-angle. We discuss the striking similarities of these
theoretical features with those found in the high- cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request;
minor revisions in the text and references have been made; To be published in
July 1 issue of Phys. Rev. B52, (1995
Statistically induced phase transitions and anyons in 1D optical lattices
Anyons-particles carrying fractional statistics that interpolate between bosons and fermions-have been conjectured to exist in low-dimensional systems. In the context of the fractional quantum Hall effect, quasi-particles made of electrons take the role of anyons whose statistical exchange phase is fixed by the filling factor. Here we propose an experimental setup to create anyons in one-dimensional lattices with fully tuneable exchange statistics. In our setup, anyons are created by bosons with occupation-dependent hopping amplitudes, which can be realized by assisted Raman tunnelling. The statistical angle can thus be controlled in situ by modifying the relative phase of external driving fields. This opens the fascinating possibility of smoothly transmuting bosons via anyons into fermions and of inducing a phase transition by the mere control of the particle statistics as a free parameter. In particular, we demonstrate how to induce a quantum phase transition from a superfluid into an exotic Mott-like state where the particle distribution exhibits plateaus at fractional densities
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