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International Conference on Strongly Correlated Electron Systems (SCES)

FFLO State and Anomalous Flux Quantization in the One-Dimensional Attractive Hubbard Models with Imbalanced Spin Populations

Kazuhiro Sano, Yoshiaki Ōno

Published Jun 16, 2014• 1 citation
Publisher

Abstract

We examine anomalous flux quantization of the one-dimensional attractive Hubbard models with imbalanced spin populations by using the exact diagonalization method. In the single chain Hubbard model with sufficiently large attractive interaction and imbalanced spin populations, the period of the flux quanta is determined by the difference between the system size N_L and electron number N_e as h/(N_L − N_e)e, in contrast to the superconducting flux quanta of h/2e based on usual Cooper pairs and/or the period h/4e derived by the mean-field theory. We find that similar anomalous flux quantization appears in the zigzag and ladder Hubbard models with imbalanced spin populations, when the band structure near the Fermi levels is regarded to be almost equivalent to that of the single chain Hubbard model.

DOI
10.7566/jpscp.3.015041

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We examine anomalous flux quantization of the one-dimensional attractive Hubbard models with imbalanced spin populations by using the exact diagonalization method. In the single chain Hubbard model with sufficiently large attractive interaction and imbalanced spin populations, the period of the flux quanta is determined by the difference between the system size N_L and electron number N_e as h/(N_L − N_e)e, in contrast to the superconducting flux quanta of h/2e based on usual Cooper pairs and/or the period h/4e derived by the mean-field theory. We find that similar anomalous flux quantization appears in the zigzag and ladder Hubbard models with imbalanced spin populations, when the band structure near the Fermi levels is regarded to be almost equivalent to that of the single chain Hubbard model.
We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with power-law decay as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization of period h=4e, half of the superconducting flux quantum of h=2e, as recently predicted by mean-field analysis, together with various flux quanta smaller than h=4e. Notably, the observed flux quanta are determined by the difference between the system size NL and electron number N_e as h=(N_L-N_e)e.
We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with power-law decays as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of the Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization with a half of the superconducting flux quantum h/4e as recently predicted by the mean-field analysis, together with various flux quanta smaller than h/4e. Remarkably, the observed flux quanta are determined by the difference between the system size N_L and the electron number N_e as h/(N_L - N_e)_e.
We investigate anomalous oscillations due to the Aharonov-Bohm(AB) and Aharonov-Casher(AC) effects of the one-dimensional Hubbard ring with flux in the strong coupling limit. By using the exact diagonalization method and the Shiba transformation, we examine the energies of the ground state and few excited states in the presence of the flux producing the AB or AC effect, where the transformation not only reverses the sign of the interaction U, but also exchanges the role between the AB and AC effects in the model Hamiltonian. We classify the number of oscillation of the ground state as a function of the flux systematically and clarify the close relationship between the AB and AC effects. For example, it is shown that the number of the periods are given by N_L - N_e(N_L - N_↑ + N_↓) for the AB(AC) effect in the very strong attraction, where N_L, N_e, N_↑, and N_↓ are the system size, the number of the total electrons, the number of electrons with up-spin, and the number of electrons with down-spin, respectively, in the condition of N_L > N_e > N_↓ > N_↑. More special case, such as the half-filled band and spin balanced case (N_L = N_e and N_↓ = N_↑ ), we find the periodicity of the system to be 0(2) for the AB(AC) effect in the very strong repulsion. These results show us the nature of interesting phenomena originated by the interplay between the strong correlation and the quantum interference effect in the mesoscopic ring.
Using the numerical diagonalization method, we investigate superconductivity and related ferromagnetism in the one-dimensional two-orbital Hubbard model with a finite band splitting at less than half filling. We obtain superconducting (SC) region with the Luttinger liquid parameter Kρ > 1 and confirm anomalous flux quantization in the SC state. It is found that the SC phase appears near partially polarized ferromagnetic phase. We also calculate various pairing correlation functions to clarify the nature of the SC phase. Detailed analysis of these functions indicates that the triplet pairing between the nearest neighbor sites is relevant to the superconductivity. It suggests that the ferromagnetic fluctuation plays an important role for the superconductivity.
We present an exact quantum Monte Carlo study of the attractive one-dimensional Hubbard model with imbalanced fermion population. The pair-pair correlation function, which decays monotonically in the absence of polarization P, develops oscillations when P is nonzero, characteristic of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. The pair momentum distribution peaks at a momentum equal to the difference in the Fermi momenta. At strong coupling, the minority and majority momentum distributions are shown to be deformed, reflecting the presence of the other species and its Fermi surface. The FFLO oscillations survive the presence of a confining potential, and the local polarization at the trap center exhibits a marked dip, similar to that observed experimentally.
We obtain a phase diagram of the spin-imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types of FFLO phases, i.e., superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the center-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the mechanism responsible for the formation of those phases, the crucial role is played by the flat band, wherein particles can readjust their density at zero energy cost. The multiorbital structure of the unit cell is found to stabilize the Sarma phase by allowing for a modulation of the order parameter within a unit cell. We also study the effect of finite temperature and a lattice with staggered hopping parameters on the behavior of these phases.