186 research outputs found
Geometrical phases and quantum numbers of solitons in nonlinear sigma-models
Solitons of a nonlinear field interacting with fermions often acquire a
fermionic number or an electric charge if fermions carry a charge. We show how
the same mechanism (chiral anomaly) gives solitons statistical and rotational
properties of fermions. These properties are encoded in a geometrical phase,
i.e., an imaginary part of a Euclidian action for a nonlinear sigma-model. In
the most interesting cases the geometrical phase is non-perturbative and has a
form of an integer-valued theta-term.Comment: 5 pages, no figure
Flat spin wave dispersion in a triangular antiferromagnet
The excitation spectrum of a S=1/2 2D triangular quantum antiferromagnet is
studied using 1/S expansion. Due to the non-collinearity of the classical
ground state significant and non-trivial corrections to the spin wave spectrum
appear already in the first order in 1/S in contrast to the square lattice
antiferromagnet. The resulting magnon dispersion is almost flat in a
substantial portion of the Brillouin zone. Our results are in quantitative
agreement with recent series expansion studies by Zheng, Fjaerestad, Singh,
McKenzie, and Coldea [PRL 96, 057201 (2006) and cond-mat/0608008].Comment: 4.1 pages, 13 figures; v2 - as published, references update
Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit
We derive an asymptotic expansion for a Wiener-Hopf determinant arising in
the problem of counting one-dimensional free fermions on a line segment at zero
temperature. This expansion is an extension of the result in the theory of
Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig
conjecture. The coefficients of this expansion are conjectured to obey certain
periodicity relations, which renders the expansion explicitly periodic in the
"counting parameter". We present two methods to calculate these coefficients
and verify the periodicity relations order by order: the matrix Riemann-Hilbert
problem and the Painleve V equation. We show that the expansion coefficients
are polynomials in the counting parameter and list explicitly first several
coefficients.Comment: 11 pages, minor corrections, published versio
Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains
We propose to describe correlations in classical and quantum systems in terms
of full counting statistics of a suitably chosen discrete observable. The
method is illustrated with two exactly solvable examples: the classical
one-dimensional Ising model and the quantum spin-1/2 XY chain. For the
one-dimensional Ising model, our method results in a phase diagram with two
phases distinguishable by the long-distance behavior of the Jordan-Wigner
strings. For the quantum XY chain, the method reproduces the previously known
phase diagram.Comment: 6 pages, section on Lee-Yang zeros added, published versio
Berry phase for ferromagnet with fractional spin
We study the double exchange model on two lattice sites with one conduction
electron in the limit of an infinite Hund's interaction. While this simple
problem is exactly solvable, we present an approximate solution which is valid
in the limit of large core spins. This solution is obtained by integrating out
charge degrees of freedom. The effective action of two core spins obtained in
the result of such an integration resembles the action of two fractional spins.
We show that the action obtained via naive gradient expansion is inconsistent.
However, a ``non-perturbative'' treatment leads to an extra term in the
effective action which fixes this inconsistency. The obtained ``Berry phase
term'' is geometric in nature. It arises from a geometric constraint on a
target space imposed by an adiabatic approximation.Comment: 11 pages, 3 figures, revtex
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