In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale,which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated w...In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale,which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated with respect to electron hopping. By solving the model exactly, we show that its ground state is fully spin-polarized at half-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result for the Hubbard model on a bipartite lattice. As a result, our exact solution strongly suggests that frustration may play an important role in causing metallic ferromagnetism.展开更多
By using the density matrix renormalization group technique, the phase diagram of the half-tilting extended Hubbard model is investigated. The conventional order parameter, the two-site entanglement entropy, and the b...By using the density matrix renormalization group technique, the phase diagram of the half-tilting extended Hubbard model is investigated. The conventional order parameter, the two-site entanglement entropy, and the block- block entanglement entropy are analyzed in detail. According to the numerical results, in the weak coupling region, an intermediate bond-order-wave （BOW） phase is shown to exist indeed between the charge-density-wave （CDW） and the spin-density-wave （SDW） phases. The critical phase transition points are determined by the singularity of the first order derivative of two-site entanglement entropy. In strong coupling region, a direct phase transition occurs from SDW phase to CDW phase, and shows discontinuous （first order） character accompanied with energy level crossing. The numerical results support the phase diagram proposed previously by some authors Sengupta et al., （2002）; Sandvik et al., （2004）; Zhang, （2004）. Therefore, the quantum entanglement is a sensitive tool to describe quantum phase transitions in strongly correlated electron systems.展开更多
基金supported by National Key Projects for Research and Development of China with Grant No. 2021YFA1400400the National Natural Science Foundation of China with Grants No. 12225407 and 12074174+2 种基金China Postdoctoral Science Foundation with Grants No. 2022M711569 and 2022T150315Jiangsu Province Excellent Postdoctoral Program with Grant No. 20220ZB5Fundamental Research Funds for the Central Universities
文摘In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale,which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated with respect to electron hopping. By solving the model exactly, we show that its ground state is fully spin-polarized at half-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result for the Hubbard model on a bipartite lattice. As a result, our exact solution strongly suggests that frustration may play an important role in causing metallic ferromagnetism.
基金Supported by the National Natural Science Foundation of China under Grant No.11047160the National Basic Research Program of China under Grant No.2009CB939901the Foundation of Tianjin Polytechnic University under Grant No.029289
文摘By using the density matrix renormalization group technique, the phase diagram of the half-tilting extended Hubbard model is investigated. The conventional order parameter, the two-site entanglement entropy, and the block- block entanglement entropy are analyzed in detail. According to the numerical results, in the weak coupling region, an intermediate bond-order-wave （BOW） phase is shown to exist indeed between the charge-density-wave （CDW） and the spin-density-wave （SDW） phases. The critical phase transition points are determined by the singularity of the first order derivative of two-site entanglement entropy. In strong coupling region, a direct phase transition occurs from SDW phase to CDW phase, and shows discontinuous （first order） character accompanied with energy level crossing. The numerical results support the phase diagram proposed previously by some authors Sengupta et al., （2002）; Sandvik et al., （2004）; Zhang, （2004）. Therefore, the quantum entanglement is a sensitive tool to describe quantum phase transitions in strongly correlated electron systems.
