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Journal of Experimental and Theoretical Physics

Generalized susceptibilities of a one-dimensional system of electrons in a magnetic field

G. E. Gurgenishvili, A. A. Nersesyan, L. A. Chobanyan

Published Jul 1, 1977• 0 citations
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The magnetic susceptibility at absolute-zero temperature for the one-dimensional Hubbard model is studied exactly as a function of the concentration of electrons by using Lieb and Wu's theory for this system. Our analysis essentially follows Griffiths's method for the magnetic susceptibility of the one-dimensional Heisenberg antiferromagnet, and is a generalization of Takahashi's calculation to the systems with an arbitrary concentration of electrons. The ground-state energy and the magnitude of local moments at each site are also studied. Combined with the results on the susceptibility, they should suggest how the effect of the Coulomb interaction on the properties of the system at low temperatures changes with the concentration of electrons.
We study the leading low-temperature dependence of magnetic susceptibility of one-dimensional electrons with a fixed total number of particles at the magnetic fields equal to zero-temperature critical values where the magnetic field induces commensurate-incommensurate quantum phase transitions. For free and repulsively interacting electrons there is only one such critical field corresponding to the transition to the fully polarized state. For attractively interacting electrons besides saturation field there is another critical field equal to the spin gap where zero-temperature magnetization sets in. For all cases, except for the lattice models at half filling, the magnetic susceptibility at critical values of magnetic field has a universal logarithmic temperature dependence, $\ensuremath{\chi}(T)=\ensuremath{\chi}(0)(1+2/ln\phantom{\rule{0.16em}{0ex}}T+\ensuremath{\cdots})$ for $T\ensuremath{\rightarrow}0$.
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.