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 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.

Apr 1, 20132 citations

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

Kazuhiro Sano, Yoshiaki Ōno

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 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.

International Conference on Strongly Correlated Electron Systems (SCES)Jun 16, 20141 citation

Anomalous Oscillations due to Aharonov–Bohm and Aharonov–Casher Effects of the One-Dimensional Hubbard Ring in the Strong Coupling Limit

Kazuhiro Sano, Yoshiaki Ōno

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.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.

Journal of the Physical Society of JapanNov 29, 20160 citations

Exact Numerical Study of Pair Formation with Imbalanced Fermion Populations

G. G. Batrouni, Miriam Huntley, V. G. Rousseau +1 more

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 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.

arXiv:0710.1353Physical Review LettersMar 21, 2008110 citations

Fulde-Ferrell-Larkin-Ovchinnikov state in the one-dimensional attractive Hubbard model and its fingerprint in spatial noise correlations

Andreas Lüscher, R. M. Noack, Andreas Martin Läuchli

We explore the pairing properties of the one-dimensional attractive Hubbard model in the presence of finite spin polarization. The correlation exponents for the most important fluctuations are determined as a function of the density and the polarization. We find that in a system with spin population imbalance, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type pairing at wave vector $Q=\ensuremath{\mid}{k}_{F,\ensuremath{\uparrow}}\ensuremath{-}{k}_{F,\ensuremath{\downarrow}}\ensuremath{\mid}$ is always dominant and there is no Chandrasekhar-Clogston limit. We then investigate the case of weakly coupled one-dimensional (1D) systems and determine the region of stability of the 1D FFLO phase. This picture is corroborated by density-matrix-renormalization-group simulations of the spatial noise correlations in uniform and trapped systems, unambiguously revealing the presence of fermion pairs with nonzero momentum $Q$ . This opens up an interesting possibility for experimental studies of FFLO states.We explore the pairing properties of the one-dimensional attractive Hubbard model in the presence of finite spin polarization. The correlation exponents for the most important fluctuations are determined as a function of the density and the polarization. We find that in a system with spin population imbalance, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type pairing at wave vector $Q=\ensuremath{\mid}{k}_{F,\ensuremath{\uparrow}}\ensuremath{-}{k}_{F,\ensuremath{\downarrow}}\ensuremath{\mid}$ is always dominant and there is no Chandrasekhar-Clogston limit. We then investigate the case of weakly coupled one-dimensional (1D) systems and determine the region of stability of the 1D FFLO phase. This picture is corroborated by density-matrix-renormalization-group simulations of the spatial noise correlations in uniform and trapped systems, unambiguously revealing the presence of fermion pairs with nonzero momentum $Q$. This opens up an interesting possibility for experimental studies of FFLO states.

arXiv:0712.1808Physical Review AJul 30, 200899 citations

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model

Song Cheng, Yuzhu Jiang, Yi-Cong Yu +2 more

We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency ΔkF (2ΔkF). Here ΔkF=π(n↑−n↓) is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch k=ΔkF, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter β representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency ΔkF (2ΔkF). Here ΔkF=π(n↑−n↓) is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch k=ΔkF, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter β representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.

arXiv:1710.08742Nuclear Physics BFeb 26, 20186 citations

Q

. This opens up an interesting possibility for experimental studies of FFLO states.