2002/04/30 by Pierluigi Contucci, Bruno Nachtergaele, Wolfgang L. Spitzer
Mathematics · Physics and Astronomy · #Anisotropy #Condensed matter physics #Critical field #Ferromagnetism #Field (mathematics) #Ground state #Hamiltonian (control theory) #Heisenberg model #Ising model #Lattice (music) #Magnetic field #Mathematics #Nonlinear Photonic Systems #Physics #Quantum mechanics #Strong Light-Matter Interactions #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #msc:82B10 #msc:82B20 #msc:82B24
paper · pdf · doi:10.1103/physrevb.66.064429
published as Phys. Rev. B., 66 (2002) 064429 · 13 pages, 8 figures
openalex publication_date 2002/08/30 · arxiv created 2002/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We investigate the effect of a magnetic field supported at a single lattice site on the low-energy spectrum of the ferromagnetic Heisenberg XXZ chain. Such fields, caused by impurities, can modify the low-energy spectrum significantly by pinning certain excitations, such as kink and droplet states. We distinguish between different boundary conditions (or sectors), the direction and also the strength of the magnetic field. E.g., with a magnetic field in the z direction applied at the origin and ++ boundary conditions, there is a critical field strength Bc (which depends on the anisotropy of the Hamiltonian and the spin value) with the following properties: for B<Bc there is a unique ground state with a gap, at the critical value Bc there are infinitely many (droplet) ground states with gapless excitations, and for B>Bc there is again a unique ground state but now belonging to the continuous spectrum. In contrast, any magnetic field with a nonvanishing component in the xy plane yields a unique ground state, which, depending on the boundary conditions, is either an (anti)kink, or an (anti)droplet state. For such fields, i.e., not aligned with the z axis, excitations always have a gap and we obtain a rigorous lower bound for that gap.