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arXiv:cond-mat/9803368 · Physical review. B, Condensed matter

Ground-state magnetization of polymerized spin chains

D. C. Cabra, Marcelo D. Grynberg

Published Jan 1, 1999• 37 citations
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Abstract

We investigate the ground-state magnetization plateaus appearing in spin-1/2 polymerized Heisenberg chains under external magnetic fields. The associated fractional quantization scenario and the exponents which characterize the opening of gapful excitations are analyzed by means of Abelian bosonization methods. Our conclusions are fully supported by the extrapolated results obtained from Lanczos diagonalizations of finite systems.

DOI
10.1103/physrevb.59.119

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We investigate the ground-state magnetization plateaus appearing in spin-12\frac{1}{2}21​ two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of NH4CuCl3{\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}NH4​CuCl3​ is discussed.
Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends continuously on the filling n. Here we detail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low-lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at low temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.
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We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ chain. A new class of magnetization plateau is obtained by means of Abelian bosonization methods which gives rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.