769 research outputs found
Replica Method for Wide Correlators in Gaussian Orthogonal, Unitary And Symplectic Random Matrix Ensembles
We calculate connected correlators in Gaussian orthogonal, unitary and
symplectic random matrix ensembles by the replica method in the 1/N-expansion.
We obtain averaged one-point Green's functions up to the next-to-leading order
O(1/N) and wide two-level correlators up to the first nontrivial order O(1/N^2)
and wide three-level correlators up to the first nontrivial order by
carefully treating fluctuations in saddle-point evaluation.Comment: LaTeX 21 pages, a new result on wide three-level correlators adde
Renormalization group approach to multiple-arc random matrix models
We study critical and universal behaviors of unitary invariant non-gaussian
random matrix ensembles within the framework of the large-N renormalization
group. For a simple double-well model we find an unstable fixed point and a
stable inverse-gaussian fixed point. The former is identified as the critical
point of single/double-arc phase transition with a discontinuity of the third
derivative of the free energy. The latter signifies a novel universality of
large-N correlators other than the usual single arc type. This phase structure
is consistent with the universality classification of two-level correlators for
multiple-arc models by Ambjorn and Akemann. We also establish the stability of
the gaussian fixed point in the multi-coupling model.Comment: 11 pages, 1 figure, LaTeX + a4.sty, epsf.st
Quantum phase transitions of the asymmetric three-leg spin tube
We investigate quantum phase transitions of the S=1/2 three-leg
antiferromagnetic spin tube with asymmetric inter-chain (rung) exchange
interactions. On the basis of the electron tube system, we propose a useful
effective theory to give the global phase diagram of the asymmetric spin tube.
In addition, using other effective theories we raise the reliability of the
phase diagram. The density-matrix renormalization-group and the numerical
diagonalization analyses show that the finite spin gap appears in a narrow
region around the rung-symmetric line, in contrast to a recent paper by
Nishimoto and Arikawa [Phys. Rev. B78, 054421 (2008)]. The numerical
calculations indicate that this global phase diagram obtained by use of the
effective theories is qualitatively correct. In the gapless phase on the phase
diagram, the numerical data are fitted by a finite-size scaling in the c=1
conformal field theory. We argue that all the phase transitions between the
gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless
universality class.Comment: 12 pages, 7 figures, 2 column, final versio
An asymptotic formula for marginal running coupling constants and universality of loglog corrections
Given a two-loop beta function for multiple marginal coupling constants, we
derive an asymptotic formula for the running coupling constants driven to an
infrared fixed point. It can play an important role in universal loglog
corrections to physical quantities.Comment: 16 pages; typos fixed, one appendix removed for quick access to the
main result; to be published in J. Phys.
Antiferromagnetic S=1/2 Heisenberg Chain and the Two-flavor Massless Schwinger Model
An antiferromagnetic S=1/2 Heisenberg chain is mapped to the two-flavor
massless Schwinger model at \theta=\pi. The electromagnetic coupling constant
and velocity of light in the Schwinger model are determined in terms of the
Heisenberg coupling and lattice spacing in the spin chain system.Comment: 3 pages. LaTex2
Gapless Excitation above a Domain Wall Ground State in a Flat Band Hubbard Model
We construct a set of exact ground states with a localized ferromagnetic
domain wall and with an extended spiral structure in a deformed flat-band
Hubbard model in arbitrary dimensions. We show the uniqueness of the ground
state for the half-filled lowest band in a fixed magnetization subspace. The
ground states with these structures are degenerate with all-spin-up or
all-spin-down states under the open boundary condition. We represent a spin
one-point function in terms of local electron number density, and find the
domain wall structure in our model. We show the existence of gapless
excitations above a domain wall ground state in dimensions higher than one. On
the other hand, under the periodic boundary condition, the ground state is the
all-spin-up or all-spin-down state. We show that the spin-wave excitation above
the all-spin-up or -down state has an energy gap because of the anisotropy.Comment: 26 pages, 1 figure. Typos are fixe
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