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 $T_c$ and phase diagrams compare very well with those obtained from more sophisticated and {\it 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.

arXiv comment12 pages, 15 figures

References in corpus (35)

• Discovery of microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x
• Nature of the superconductor-insulator transition in disordered superconductors
• Inhomogeneous Pairing in Highly Disordered s-wave Superconductors
• Mixed-State Quasiparticle Spectrum for d-wave Superconductors
• Pseudogap in a thin film of a conventional superconductor
• The Higgs Mode in Disordered Superconductors Close to a Quantum Phase Transition
• An exactly solvable model of the BCS-BEC crossover
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Fermions in 2D Optical Lattices: Temperature and Entropy Scales for Observing Antiferromagnetism and Superfluidity
• Dynamical band flipping in fermionic lattice systems: An ac-field-driven change of the interaction from repulsive to attractive
• Dynamical mean-field theory for pairing and spin gap in the attractive Hubbard model
• Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity
• Critical temperature for the two-dimensional attractive Hubbard Model
• Classical Phase Fluctuations in High Temperature Superconductors
• Energetic balance of the superconducting transition across the BCS-Bose E instein crossover in the attractive Hubbard model
• Critical Temperature Curve in the BEC-BCS Crossover
• Nanometer Scale Mapping of the Density of States in an Inhomogeneous Superconductor
• The Josephson effect throughout the BCS-BEC crossover
• Monte Carlo Simulations for the Magnetic Phase Diagram of the Double Exchange Hamiltonian
• Quantum Monte Carlo Study of the Disordered Attractive Hubbard Model
• Dynamical Conductivity Across The Disorder-Tuned Superconductor-Insulator Transition
• Anomalous gap edge dissipation in disordered superconductors on the brink of localization
• Non-perturbative approach to the attractive Hubbard model
• Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover
• Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model
• Parallelized Traveling Cluster Approximation to Study Numerically Spin-Fermion Models on Large Lattices
• Zn-impurity effect and interplay of $s_{\pm }$- and $s_{++}$-pairings in Fe-based superconductors
• Thermal Phase Transition in Two-Dimensional Disordered Superconductors: Kosterlitz-Thouless vs Percolation
• Double Exchange Models: Self Consistent Renormalisation
• How to measure the spatial correlations in disordered Berezinski-Kosterlitz-Thouless transition ?
• A real space auxiliary field approach to the BCS-BEC crossover
• The effect of amplitude fluctuations on the BKT transition
• Topological quantum phase transition in the BEC-BCS crossover phenomena
• BCS-BEC Crossover in the Two-Dimensional Attractive Hubbard Model: Variational Cluster Approach
• Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits

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