Effective Hamiltonian based Monte Carlo for the BCS to BEC crossover in the attractive Hubbard model

Abstract

We present an effective Hamiltonian based real-space approach for studying the weak-coupling Bardeen-Cooper-Schrieffer (BCS) to the strong-coupling Bose-Einstein condensate (BEC) crossover in the two-dimensional attractive Hubbard model at finite temperatures. We introduce and justify an effective classical Hamiltonian to describe the thermal fluctuations of the relevant auxiliary fields. Our results for Tc and phase diagrams compare very well with those obtained from more sophisticated and cpu-intensive numerical methods. We demonstrate that the method works in the presence of disorder and is useful for a real-space description of the effect of disorder on superconductivity. From a combined analysis of the superconducting order parameter, the distribution of auxiliary fields and the quasiparticle density of states, we identify the regions of metallic, insulating, superconducting and pseudogapped behavior. Our finding of the importance of phase fluctuations for the pseudogap behavior is consistent with the conclusions drawn from recent experiments on NbN superconductors. The method can be generalized to study superconductors with non-trivial order parameter symmetries by identifying the relevant auxiliary variables.

Impurity Induced Phase Competition and Supersolidity

“…The effects of disorder on the Hubbard model have been extensively studied 18,[21][22][23] . Notably, at the SO(3) symmetric point, random on-site potentials were shown to destroy CDW while sparing SC order 24 .…”

Thermodynamic evidence for electron correlation-driven flattening of the quasiparticle bands in the high-Tc cuprates

“…There are also a number of physical phenomena in hole-doped cuprates that are consistent with strong pairing interactions [5][6][7][8][9][10][11], suggesting therefore a possible role of phase fluctuations in constraining the maximum value of the critical temperature T c [12][13][14][15][16][17]. In a tight-binding lattice, phase fluctuations are predicted to cause the upper limit for the transition temperature to be given by k B T c /t ∼ 0.2 [18][19][20][21][22][23][24], where t is the in-plane hopping. Given the large value of t ≈ 360 meV predicted by electronic structure theory in the cuprates [25][26][27][28], a significant band renormalization is required for the upper limit of T c to have been reached [4].…”

“…Finally, the reduced t implies that k B T c /t ≈ 0.1, which means that the pairing is sufficiently strong for T c to be in a regime where phase fluctuations start to become an important consideration [8,[11][12][13]. Because the maximum theoretical ratio k B T c /t ≈ 0.2 [18][19][20][21][22][23][24] is based on the superfluid density of the large unreconstructed Fermi surface, a reduction in the superfluid density of the magnitude reported by Uemura et al [9,10] will be more than sufficient to give rise to a Brezinksii-Kosterlitz-Thouless transition or drive the superconductivity into the Bose pairing regime [13,14]. Possible causes include the proximity to an insulating state [85] or the reconstruction of the Fermi surface into small pockets [36,[55][56][57][58][59].…”