Properties of One-Dimensional Strongly Correlated Electrons

Abstract

There are two fundamental models for one-dimensional strongly correlated electrons: the Hubbard model and the t-] model. Recent intensive efforts have led to clarifying many important aspects of those systems, whose low-energy behaviors can be described as Luttinger liquid. This paper reviews current status of our understanding, which has been achieved with analytic and numerical approaches.

Ground-state phase diagram of the one-dimensional dimerizedt−Jmodel at quarter filling

“…1; ij stands for nearest-neighbor bonds with parameters t 1 and J 1 and kl for those with parameters t 2 (≥t 1 ) and J 2 (≥J 1 ). The model tends to the usual t−J model when there is no dimerization (t 1 =t 2 and J 1 =J 2 ), of which much study has been made [7][8][9][10], whereas in the limit of strong dimerization, the model represents an assembly of isolated dimers. We retain the relations between parameters t and J obtained from perturbation, i.e., J 1 =4t 2 1 /U and J 2 =4t 2 2 /U , in order to reduce the number of parameters, where U is the corresponding on-site Hubbard interaction.…”

Exact and Self-Consistent Results in One-Dimensional Repulsive Hubbard Model

“…The GSCF relation for the wave number q = πn at U/t 1 is consistent with the exact result for the lattice momentum q in two-particle correlation function. 36,56,57 At large U/t 1 limit from the GSCF approach we find lim U/t→∞…”

“…The relationship (A.6) is in agreement with the Luttinger theorem for the corresponding lattice momentum in the spin-spin correlation function. 36,[55][56][57] Appendix B. Ground State Energy and Chemical Potential in the Exact Theory…”

“…This result implicitly assumes that k 0 and q = W Fermi at n = 1 and h = 0 are both unrenormalized by U/t as in the exact theory. 36,[55][56][57] It is also from (33) clear that k 0 within the GSCF approach is renormalized by U/t, whenever h = 0. Earlier we studied the crossover from the itinerant BCS state into the Bose condensation regime within the attractive Hubbard model with h = 0.…”

Binding of Holons and Spinons in the One-Dimensional Anisotropict−JModel

“…It is well known [6,7] that the energies of individual spinons and holons can be obtained from GSEs of odd-L periodic chains with no holes and one hole, respectively. The even-L periodic chain with one hole contains the spinon-holon pair.…”