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Journal of Physics Conference Series

Spin instability and phase diagram of v = 2 quantum Hall systems

Kanako Yoshizawa, Kazuo Takayanagi

Published Mar 1, 2009• 0 citations
Publisher

Abstract

We present the magnetic phase diagram on the ( r a , E z ) plane in the self-consistent Hartree-Fock theory for the ν = 2 quantum Hall system. We show that there is an area on the ( r s , E z ) plane where a spiral spin density wave state is the ground state of the system.
DOI
10.1088/1742-6596/150/4/042242

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The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher dimensional Hubbard models and the J1−J2J_{1}-J_{2}J1​−J2​ Heisenberg model.
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