arXiv subjects

Christoph P. Hofmann

Publications and source records attributed to Christoph P. Hofmann.

45 records · Page 3Linked to original sources

arXiv2010

Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics and the 1/N approximation

We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient $θ$ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening --characteristic of the 1/N approximation-- is observed in the entire $(N,θ)$-plane through the local and global properties of the vector part of the fermion propagator.

hep-ph↗

arXiv2009

Collocation method for fractional quantum mechanics

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on Little Sinc Functions (LSF), which discretizes the Schrödinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a WKB analysis is performed.

quant-ph↗

arXiv2009

Thermodynamics of O(N) Antiferromagnets in 2+1 Dimensions

Within the framework of effective Lagrangians we calculate the free energy density for an O($N$) antiferromagnet in 2+1 dimensions up to three-loop order in the perturbative expansion and derive the low-temperature series for various thermodynamic quantities. In particular, we show that the magnon-magnon interaction in the O(3) antiferromagnet in $d$=2+1 -- the O(3)-invariant quantum Heisenberg antiferromagnet on a square or a honeycomb lattice -- is very weak and repulsive and manifests itself through a term proportional to five powers of the temperature in the free energy density. Remarkably, the corresponding coefficient is fully determined by the leading-order effective Lagrangian ${\cal L}^2_{eff}$ and does not involve any higher order effective constants from ${\cal L}^4_{eff}$ related to the anisotropies of the lattice -- the symmetries are thus very restrictive in $d$=2+1. We also compare our results that apply to O($N$) antiferromagnets in 2+1 dimensions with the those for O($N$) antiferromagnets in 3+1 dimensions. The present work demonstrates the efficiency of the fully systematic effective Lagrangian method in the condensed matter domain, which clearly proves to be superior to spin-wave theory. We would like to emphasize that the structure of the low-temperature series derived in the present work is model-independent and universal as it only relies on symmetry considerations.

cond-mat.str-el↗

arXiv2006

Renormalization of the baryon axial vector current in large-N_c chiral perturbation theory

The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large-N_c limit, where N_c is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in N_c as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. These cancellations are explicitly shown for the general case of N_f flavors of light quarks. In particular, a new generic cancellation is identified in the renormalization of the baryon axial vector current at one-loop order. A comparison with conventional heavy baryon chiral perturbation theory is performed at the physical values N_c=3, N_f=3.

hep-ph↗

arXiv2002

Ferromagnets and antiferromagnets in the effective Lagrangian perspective

Nonrelativistic systems exhibiting collective magnetic behavior are analyzed within the framework of effective Lagrangians. The method, which formulates the dynamics of the system in terms of Goldstone bosons, allows to investigate the consequences of spontaneous symmetry breaking from a unified point of view. Analogies and differences with respect to the Lorentz-invariant situation (chiral perturbation theory) are pointed out. We then consider the low-temperature expansion of the partition function both for ferro- and antiferromagnets, where the spin waves or magnons represent the Goldstone bosons of the spontaneously broken symmetry $O(3) \to O(2)$. In particular, the low-temperature series of the staggered magnetization for antiferromagnets and the spontaneous magnetization for ferromagnets are compared with the condensed matter literature.

cond-mat↗

arXiv2001

Spontaneous Magnetization of the O(3) Ferromagnet at Low Temperatures

We investigate the low-temperature behavior of ferromagnets with a spontaneously broken symmetry O(3) $\to$ O(2). The analysis is performed within the perspective of nonrelativistic effective Lagrangians, where the dynamics of the system is formulated in terms of Goldstone bosons. Unlike in a Lorentz-invariant framework (chiral perturbation theory), where loop graphs are suppressed by two powers of momentum, loops involving ferromagnetic spin waves are suppressed by three momentum powers. The leading coefficients of the low-temperature expansion for the partition function are calculated up to order $p^{10}$. In agreement with Dyson's pioneering microscopic analysis of the cubic ferromagnet, we find that, in the spontaneous magnetization, the magnon-magnon interaction starts manifesting itself only at order $T^4$. The striking difference with respect to the low-temperature properties of the O(3) antiferromagnet is discussed from a unified point of view, relying on the effective Lagrangian technique.

cond-mat↗

arXiv2000

Spin-wave Scattering in the Effective Lagrangian Perspective

Nonrelativistic systems exhibiting collective magnetic behavior are analyzed in the framework of effective Lagrangians. The method, formulating the dynamics in terms of Goldstone bosons, allows to investigate the consequences of spontaneous symmetry breaking from a unified point of view. Low energy theorems concerning spin-wave scattering in ferro- and antiferromagnets are established, emphasizing the simplicity of actual calculations. The present work includes approximate symmetries and discusses the modification of the low energy structure imposed by an external magnetic and an anisotropy field, respectively. Throughout the paper, analogies between condensed matter physics and Lorentz-invariant theories are pointed out, demonstrating the universal feature of the effective Lagrangian technique.

cond-mat↗

arXiv2000

Effective Analysis of the O(N) Antiferromagnet: Low Temperature Expansion of the Order Parameter

We investigate the low energy properties of Lorentz-invariant theories with a spontaneously broken rotation symmetry O(N) $\to$ O(N--1). The leading coefficients of the low temperature expansion for the partition function are calculated up to and including three loops. Emphasis is put into the special case N=3: it describes the antiferromagnet which has been extensively studied. Our results obtained within the framework of the effective Lagrangian technique are compared with the literature. In particular, we show that, at order $T^7$ for the heat capacity and $T^6$ for the order parameter, respectively, logarithmic terms appear in the low temperature expansion, which have been overlooked so far.

hep-ph↗

arXiv2000

On the structure of large N cancellations in baryon chiral perturbation theory

We show how to compute loop graphs in heavy baryon chiral perturbation theory including the full functional dependence on the ratio of the Delta--nucleon mass difference to the pion mass, while at the same time automatically incorporating the 1/N cancellations that follow from the large-N spin-flavor symmetry of baryons in QCD. The one-loop renormalization of the baryon axial vector current is studied to demonstrate the procedure. A new cancellation is identified in the one-loop contribution to the baryon axial vector current. We show that loop corrections to the axial vector currents are exceptionally sensitive to deviations of the ratios of baryon-pion axial couplings from SU(6) values.

hep-ph↗