The interplay between d-wave superconductivity and antiferromagnetic fluctuations: a quantum Monte Carlo study

We consider the repulsive Hubbard model on a square lattice with an additional term, W, which depends upon the square of a single-particle nearest-neighbor hopping. At half-band filling, constant W, we show that enhancing U/t drives the system from a d-wave superconductor to an antiferromagnetic Mott insulator. At zero temperature in the superconducting phase, spin-spin correlations follow a powerlaw: e-ir.Q|r|-α. Here Q= (π,π) and α is in the range 1 < α < 2 and depends upon the coupling constants W and U. This results is reached on the basis of large scale quantum Monte-Carlo simulations on lattices up to 24 × 24, and is shown to be independent on the choice of the boundary conditions. We define a pairing (magnetic) scale by the temperature below which short range d-wave pairing correlations (antiferromagnetic fluctuations) start growing. With finite temperature quantum Monte Carlo simulations, we demonstrate that both scales are identical over a large energy range. Those results show the extreme compatibility and close interplay of antiferromagnetic fluctuations and d-wave superconductivity.The understanding of the interplay between d-wave superconductivity and antiferromagnetism is a central issue for the understanding of the phase diagram of High-T _c superconductors [1]. The aim of this work is to further study a model which shows a quantum transition between a d-wave superconductor and an antiferromagnetic Mott insulator. It thus enables us to address the above question. The model we consider, has been introduced in Ref. [2]. It is defined by: 1$$ H = - \frac{t}{2}\sum\limits_i {{K_i}} - W\sum\limits_i {K_i^2} + U\sum\limits_i {\left( {{n_{i, \uparrow }} - \frac{1}{2}} \right)} \left( {{n_{i, \downarrow }} - \frac{1}{2}} \right) $$ with the hopping kinetic energy 2$${{K}_{i}} = \sum\limits_{{\sigma ,\delta }} {(c_{{i,\sigma }}^{\dag }{{c}_{{i + \delta ,\sigma }}} + c_{{i + \delta ,\sigma }}^{\dag }{{c}_{{i,\sigma }}})}$$ Here, W ≥ 0, δ = ±a _x , ±a _y , and n _i,σ = c _i,σ †c _i,σ where c _i,σ †(c _i,σ ) creates (annihilates) an electron on site i with z-component of spin σ. We impose twisted boundary conditions: 3$$ {c_{i + L{a_x},\sigma }} = \exp \left( {2\pi i\Phi /{\Phi _0}} \right){c_{i,\sigma }},{c_{i + L{a_y},\sigma }} = {c_{i,\sigma }} $$We have equally shown that the energy scales at which d-wave pairing and antiferromagnetic fluctuations occur are identical. The further understanding of spin and charge dynamics, as well as the doping of the model remains for further studies.