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