Phase Transitions and Magnetic Ordering in the 1D Hubbard Chain

The phase transitions and magnetic ordering of the one dimensional spin-1/2 Hubbard chain are studied as a function of the next nearest neighbor hopping and onsite interaction using DMRG. At large U, this model maps to a Majumdar-Ghosh chain with known Kosterlitz-Thouless transition(KT point) at J₂/J₁ ∼ 0.2411 and commensurate-incommensurate transition(Disorder(DO) point) at J₂/J₁ = 0.5, prompting the investigation of such points within the low-U limit. Extending the methods used in Heisenberg spin chains to the Hubbard model, the velocity as well as the central charge are calculated for different values of t₂ and U in order to deduce the KT point. Similarly, the spin correlation function 〈S_{N/2 + 1} S_{i + N/2 + 1}〉 is found and fitted to the dimerized Ornstein-Zernicke form to determine the correlation length, with the location of the minimum indicating the DO point. Preliminary analysis for U = 4 shows a KT point at t₂/t₁ ∼ 0.564 and a DO point at t₂/t₁ ∼ 0.68. Future work will include an extensive study of the migration of these points as a function of U.