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arXiv:cond-mat/0008333 · Physical review. B, Condensed matter

Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains

D. C. Cabra, Alessandro De Martino, A. Honecker, Pierre Pujol, Pascal Simon

Published Jan 30, 2001• 20 citations

Abstract

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.

DOI: 10.1103/physrevb.63.094406

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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.

We study the behavior of magnetization curve as a function of magnetic field in the immediate vicinity of the magnetization plateaus of one-dimensional (1D) electron systems within the bosonization formalism. First we discuss the plateau that is formed at the saturation magnetization of 1D electron system. We treat interactions between electrons in the lowest order of perturbation. We show that for isolated systems, where total number of electrons is not allowed to vary, magnetic susceptibility stays always finite away of half filling. Similar statement holds for many other magnetization plateaus supporting nonmagnetic gapless excitations encountered in 1D electron/spin systems in the absence of special symmetries or features responsible for the mode decoupling. We demonstrate it on example of the plateaus at irrational values of magnetization in doped modulated Hubbard chains. Finally we discuss the connection between the weak coupling description of saturation magnetization plateau and strong coupling description of zero magnetization plateau of attractively interacting electrons.

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We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin,

S

, the magnetization curve can have plateaus and we argue that the magnetization per site

m

is topologically quantized as $n(S\ensuremath{-}m)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{integer}$ at the plateaus, where

n

is the period of the ground state. We also discuss conditions for the presence of the plateau at those quantized values. For

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2

and

m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer

S

.

We report results of theoretical investigations on the effect of doping and quenched disorder on the occurrence of plateaux in the magnetization curve of 1D systems with periodic modulations in the couplings.For single q-merized Hubbard chains, doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distributions.In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.

The low-temperature magnetization process of antiferromagnetic spin-

S

chains doped with mobile spin- $(S\ensuremath{-}1/2)$ carriers is studied in an exactly solvable model. For sufficiently high magnetic fields the system is in a metallic phase with a finite gap for magnetic excitations. In this phase, which exists for a large range of carrier concentrations

x

, the zero-temperature magnetization is determined by

x

alone. This leads to plateaus in the magnetization curve at a tunable fraction of the saturation magnetization. The critical behavior at the edges of these plateaus is studied in detail.

We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.