34 research outputs found
Exact density matrix of the Gutzwiller wave function: II. Minority spin component
The density matrix, i.e. the Fourier transform of the momentum distribution,
is obtained analytically for all magnetization of the Gutzwiller wave function
in one dimension with exclusion of double occupancy per site. The present
result complements the previous analytic derivation of the density matrix for
the majority spin. The derivation makes use of a determinantal form of the
squared wave function, and multiple integrals over particle coordinates are
performed with the help of a diagrammatic representation. In the thermodynamic
limit, the density matrix at distance x is completely characterized by
quantities v_c x and v_s x, where v_s and v_c are spin and charge velocities in
the supersymmetric t-J model for which the Gutzwiller wave function gives the
exact ground state. The present result then gives the exact density matrix of
the t-J model for all densities and all magnetization at zero temperature.
Discontinuity, slope, and curvature singularities in the momentum distribution
are identified. The momentum distribution obtained by numerical Fourier
transform is in excellent agreement with existing result.Comment: 20 pages, 10 figure
Exact Dynamics of the SU(K) Haldane-Shastry Model
The dynamical structure factor of the SU(K) (K=2,3,4)
Haldane-Shastry model is derived exactly at zero temperature for arbitrary size
of the system. The result is interpreted in terms of free quasi-particles which
are generalization of spinons in the SU(2) case; the excited states relevant to
consist of K quasi-particles each of which is characterized by a
set of K-1 quantum numbers. Near the boundaries of the region where
is nonzero, shows the power-law singularity. It is
found that the divergent singularity occurs only in the lowest edges starting
from toward positive and negative q. The analytic result
is checked numerically for finite systems via exact diagonalization and
recursion methods.Comment: 35 pages, 3 figures, youngtab.sty (version 1.1
Topological quantum phase transition in the BEC-BCS crossover phenomena
A crossover between the Bose Einstein condensation (BEC) and BCS
superconducting state is described topologically in the chiral symmetric
fermion system with attractive interaction. Using a local Z_2 Berry phase, we
found a quantum phase transition between the BEC and BCS phases without
accompanying the bulk gap closing.Comment: 4 pages, 5 figure
Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band
While usual edge states in the quantum Hall effect(QHE) reside between
adjacent Landau levels, QHE in graphene has a peculiar edge mode at E=0 that
reside right within the n=0 Landau level as protected by the chiral symmetry.
We have theoretically studied the edge states to show that the E=0 edge mode,
despite being embedded in the bulk Landau level, does give rise to a wave
function whose charge is accumulated along zigzag edges. This property, totally
outside continuum models, implies that the graphene QHE harbors edges distinct
from ordinary QHE edges with their topological origin. In the charge
accumulation the bulk states re-distribute their charge significantly, which
may be called a topological compensation of charge density. The real space
behavior obtained here should be observable in an STM imaging.Comment: 4 pages, 9 figure
Basic properties of three-leg Heisenberg tube
We study three-leg antiferromagnetic Heisenberg model with the periodic
boundary conditions in the rung direction. Since the rungs form regular
triangles, spin frustration is induced. We use the density-matrix
renormalization group method to investigate the ground state. We find that the
spin excitations are always gapped to remove the spin frustration as long as
the rung coupling is nonzero. We also visibly confirm spin-Peierls dimerization
order in the leg direction. Both the spin gap and the dimerization order are
basically enhanced as the rung coupling increases.Comment: 4 pages, 2 figure