2008/04/30 by Andreas Kreisel, Francesca Sauli, N. Hasselmann +2 · 4 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.78.035127
published as Phys. Rev. B 78, 035127 (2008) · 19 pages, 4 figures
openalex publication_date 2008/07/28 · arxiv created 2008/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reexamine the 1/S correction to the self-energy of the gapless magnon of a D-dimensional quantum Heisenberg antiferromagnet in a uniform magnetic field h using a hybrid approach between 1/S expansion and nonlinear sigma model, where the Holstein-Primakoff bosons are expressed in terms of Hermitian field operators representing the uniform and the staggered components of the spin operators [N. Hasselmann and P. Kopietz, Europhys. Lett. 74, 1067 (2006)]. By integrating over the field associated with the uniform spin fluctuations, we obtain the effective action for the staggered spin fluctuations on the lattice, which contains fluctuations on all length scales and does not have the cutoff ambiguities of the nonlinear sigma model. We show that in dimensions D\ensuremath≤3, the magnetic-field dependence of the spin-wave velocity \stackrel\ifmmode \else \~\fic_\ensuremath-(h) is nonanalytic in h2, with \stackrel\ifmmode \else \~\fic_\ensuremath-(h)\ensuremath-\stackrel\ifmmode \else \~\fic_\ensuremath-(0)\ensuremath∝h2 ln|h| in D=3, and \stackrel\ifmmode \else \~\fic_\ensuremath-(h)\ensuremath-\stackrel\ifmmode \else \~\fic_\ensuremath-(0)\ensuremath∝|h| in D=2. The frequency-dependent magnon self-energy is found to exhibit an even more singular magnetic-field dependence, implying a strong momentum dependence of the quasiparticle residue of the gapless magnon. We also discuss the problem of spontaneous magnon decay and show that in D>1 dimensions, the damping of magnons with momentum \mathbitk is proportional to |\mathbitk|^2D\ensuremath-1 if spontaneous magnon decay is kinematically allowed.