We report the results of zero-temperature quantum Monte Carlo simulations and zero-temperature mean-field calculations of the attractive Hubbard model on chains, ladders, and square lattices. We investigated the predictability of the BCS approximation, the dimensional crossover of the pairing correlation function from one to two dimensions as a function of the ladder width, and the scaling of these correlations to the thermodynamic limit of the two-dimensional model. We found that the BCS wave function is quantitatively correct only for small values of $U/t.$ For the system sizes, electron fillings, and interaction strengths studied, we never saw the dimensional crossover. In general, our ability to achieve the dimensional crossover and accurate scaling to the thermodynamic limit was limited by the size of the systems we could simulate. For these sizes, although we saw the necessary signature of off-diagonal long-range order, the properties of the model did not vary monotonically with increasing system size because of shell effects. We contrast this situation with the dimensional crossover and scaling to the thermodynamic limit of the Ising model.We report the results of zero-temperature quantum Monte Carlo simulations and zero-temperature mean-field calculations of the attractive Hubbard model on chains, ladders, and square lattices. We investigated the predictability of the BCS approximation, the dimensional crossover of the pairing correlation function from one to two dimensions as a function of the ladder width, and the scaling of these correlations to the thermodynamic limit of the two-dimensional model. We found that the BCS wave function is quantitatively correct only for small values of $U/t.$ For the system sizes, electron fillings, and interaction strengths studied, we never saw the dimensional crossover. In general, our ability to achieve the dimensional crossover and accurate scaling to the thermodynamic limit was limited by the size of the systems we could simulate. For these sizes, although we saw the necessary signature of off-diagonal long-range order, the properties of the model did not vary monotonically with increasing system size because of shell effects. We contrast this situation with the dimensional crossover and scaling to the thermodynamic limit of the Ising model.

arXiv:cond-mat/9912114Physical review. B, Condensed matterJul 1, 200022 citations

Pairing features of electrons in BE-BCS regimes in two dimensional systems

D. Volčko

Jan 1, 20010 citations

Phase diagram and BCS-Bose condensation crossover in 1D and 2D Hubbard models

Kocharian AN; Yang C; Chiang YL, Yang L; Yeh SD; Xie S; Altuwaijri S; Ni J; Hu YC; Chen YT; Bao BY; Su CH; Chang C, Y L Chiang

[[abstract]]The ground-state energy, the concentration of double occupied sites and the density of bound electron pairs in low-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach. This approach gives an excellent agreement with the corresponding Bethe-ansatz solution and the quantum Monte-Carlo calculations in a wide range of interaction strength U < 0 and electron concentration n. A simple relationship is found between the order parameter and the density of bound electron pairs, valid for any dimension and in entire parameter space U, n and magnetic field h. The electron pairing and the crossover from the itinerant BCS regime into the Bose condensation regime of local pairs are studied in dependence of both U and n. The GSCF theory correctly displays the separation of the energy gap from the BCS order parameter at n not equal 1 as \U \ increases. (C) 2001 Elsevier Science B.V. All rights reserved.[[abstract]]The ground-state energy, the concentration of double occupied sites and the density of bound electron pairs in low-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach. This approach gives an excellent agreement with the corresponding Bethe-ansatz solution and the quantum Monte-Carlo calculations in a wide range of interaction strength U < 0 and electron concentration n. A simple relationship is found between the order parameter and the density of bound electron pairs, valid for any dimension and in entire parameter space U, n and magnetic field h. The electron pairing and the crossover from the itinerant BCS regime into the Bose condensation regime of local pairs are studied in dependence of both U and n. The GSCF theory correctly displays the separation of the energy gap from the BCS order parameter at n not equal 1 as \U \ increases. (C) 2001 Elsevier Science B.V. All rights reserved.

Jan 1, 20010 citations

The pairing symmetries in the two-dimensional Hubbard model

Ke Liu, Shuhui Yang, Weiqi Li +4 more

Physics Letters AJan 8, 20214 citations

d-wave Pairing in the Two-Dimensional Hubbard Model

Douglas J. Scalapino

Bulletin of the American Physical SocietyMar 14, 20060 citations

Pairing Fluctuations and Anomalous Transport Above the BCS-BEC Crossover in the Two Dimensional Attractive Hubbard Model

Sabyasachi Tarat, Pinaki Majumdar

A Fermi liquid with weak attractive interaction undergoes a BCS transition to a superconductor with reducing temperature. With increasing interaction strength, the thermal transition is progressively modified as the high temperature `metallic' phase develops a pseudogap due to pairing fluctuations and the resistivity above T_c shows insulating behaviour. The crossover to insulating character occurs much before the system can be considered to be in the BEC regime of preformed fermion pairs. We use a new Monte Carlo tool to map out the BCS-BEC crossover in the attractive Hubbard model on large two dimensional lattices and explicitly compute the resistivity to demonstrate how the metal to superconductor (MS) thermal transition at weak coupling crosses over to an insulator to superconductor (IS) transition at intermediate coupling. Our high resolution access to the single particle and optical spectrum at finite temperature allows us to completely describe the transport crossover in this longstanding problem.A Fermi liquid with weak attractive interaction undergoes a BCS transition to a superconductor with reducing temperature. With increasing interaction strength, the thermal transition is progressively modified as the high temperature `metallic' phase develops a pseudogap due to pairing fluctuations and the resistivity above T_c shows insulating behaviour. The crossover to insulating character occurs much before the system can be considered to be in the BEC regime of preformed fermion pairs. We use a new Monte Carlo tool to map out the BCS-BEC crossover in the attractive Hubbard model on large two dimensional lattices and explicitly compute the resistivity to demonstrate how the metal to superconductor (MS) thermal transition at weak coupling crosses over to an insulator to superconductor (IS) transition at intermediate coupling. Our high resolution access to the single particle and optical spectrum at finite temperature allows us to completely describe the transport crossover in this longstanding problem.

arXiv:1105.1156May 5, 20110 citations

U/t.

For the system sizes, electron fillings, and interaction strengths studied, we never saw the dimensional crossover. In general, our ability to achieve the dimensional crossover and accurate scaling to the thermodynamic limit was limited by the size of the systems we could simulate. For these sizes, although we saw the necessary signature of off-diagonal long-range order, the properties of the model did not vary monotonically with increasing system size because of shell effects. We contrast this situation with the dimensional crossover and scaling to the thermodynamic limit of the Ising model.