We study the phase diagram of the Hubbard model in the limit where U, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for T$_c$, the superconducting transition temperature, in terms of the correlation functions of the non-interacting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing T$_c$ involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff $Ω_0$. Then, the renormalization group (RG) flows of the resulting effective action are computed and T$_c$ is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that T$_c$ is independent of $Ω_0$. Using this method, we find a variety of unconventional superconducting ground states in two and three dimensional lattice systems and present explicit results for T$_c$ and pairing symmetries as a function of the electron concentration.
Perturbation Theory for a Repulsive Hubbard Model in Quasi-One-Dimensional Superconductors
研究了准一维排斥哈伯德模型的对对称性和相变温度。我们用三阶微扰展开法求解了Eliashberg方程，并考虑了在位排斥$U$ .我们发现，当电子数密度从半充满的，过渡到非常规超导预期。当一维性较弱时，自旋单重态是有利的。相比之下，当一维性强且电子数密度远离半填充时，自旋三重态稳定。最后，我们讨论了在$β$ -Na $_{0.33}$ V $_2$ O $_5$中由在位库仑排斥引起的非常规超导电性的可能性。
With the discovery of strong coupling physics and superconductivity in Moiré superlattices, it's essential to have an understanding of strong coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here we use density matrix renormalization group (DMRG) to investigate the domininant superconducting channels in the hole-doped…
We introduce a new and general mechanism for superconductivity in Fermi systems with strong repulsive interaction. Because kinetic terms are small compared to the bare repulsion, the dynamic of charge carriers is constrained by the the presence of other nearby carriers. By treating kinetic terms as a perturbation around the atomic limit, we show that pairing can be induced by correlated multi-particle tunneling processes that favor two itinerant carriers to be close together. Our analytically-controlled theory provides a quantitative formula relating $T_c$ to microscopic parameters, with maxim…
Perturbation Analysis of Superconductivity in the Trellis-Lattice Hubbard Model
我们研究了格子哈伯德模型中的对对称性和相变温度。利用三阶微扰理论求解了考虑在位排斥$U$的Eliashberg方程。我们发现自旋单重态在很宽的参数范围内是非常稳定的。另一方面，当电子数密度从半填充状态偏移并且两个带之间的带隙小时，预期自旋三重态超导性。最后讨论了Sr $_{14-x}$ Ca $_x$ Cu $_{24}$ O $_{41}$的非常规超导电性和对对称性的可能性。
We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the non-interacting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger type interaction, while the pairing symmetry of the bands are indirectly a…
In a recent preprint [arXiv:1803.04118v2] Chern and Barros report numerical simulations of the mean-field interaction quench dynamics, $U_i\to U_f$, of the attractive Hubbard model that confirm our earlier prediction [Europhys. Lett. 85, 20004 (2008), arXiv:0805.2798] of spontaneous eruption of spatial inhomogeneities in the post-quench state with periodically oscillating superconducting order. Chern and Barros attribute this instability with respect to spatial fluctuations to the large magnitude of the final Hubbard coupling $U_f$. We point out that this interpretation is inaccurate and discu…
We study a three-dimensional single-band repulsive Hubbard model at weak coupling. We establish the superconducting phase diagram in the parameter space of the chemical potential and the out-of-plane hopping strength. The model continuously connects the Hubbard model in two and three dimensions. We confirm previously-established results in these limits, and identify a rich structure of competing order parameters in between. Specifically, we find five types of $p$- and $d$-wave orders. In several regions of the phase diagram, even when the Fermi surface is a corrugated cylinder, the ground stat…
We review recent theoretical progress in understanding spatially uniform $s$-wave superconductivity which arises from a fermion-fermion interaction, which is repulsive on the Matsubara axis, where it is real, but does depend on the transferred frequency. Such a situation holds, e.g., for systems with a screened Coulomb and retarded electron-phonon interaction. We show that despite repulsion, superconductivity is possible in a certain range of system parameters. However, at $T=0$ the gap function on the Matsubara axis, $Δ(ω_m)$, must pass through zero and change sign at least once. These zeros …
Heterostructures containing strongly correlated electron systems provide a platform to clarify interplay of electron correlation and Rashba spin-orbit coupling in unconventional superconductors. Motivated by recent fabrication of artificially-engineered heavy fermion superlattices and high-temperature cuprate superconductors, we conduct a thorough study on superconductivity in Rashba-Hubbard model. In contrast to previous weak coupling approaches, we employ fluctuation-exchange approximation to describe quantum critical magnetic fluctuations and resulting superconductivity. As a result, robust…
We show that the extended attractive Hubbard model on a square lattice hosts a variety of superconducting phases, including exotic mixed-symmetry phases with $d_{x^2-y^2} + {\rm i} [s + d_{x^2+y^2}]$ and $ d_{x^2-y^2} + p_{x}$ symmetries, and a novel $p_x + {\rm i} p_y$ state. The calculations are performed within the mean-field Bogoliubov-deGennes (BdG) framework. The ground states of the BdG Hamiltonian are obtained via a minimization scheme that does not impose symmetry constraints on the superconducting solutions, hence allowing a mixing of $s$-, $p$- and $d$-wave order parameters. Our res…
Superconductivity from purely repulsive interactions in the strong coupling approach : Application of the SU(2) slave-rotor theory to the Hubbard model
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.
Motivated by a scarcity of simple and analytically tractable models of superconductivity from strong repulsive interactions, we introduce a simple tight-binding lattice model of fermions with repulsive interactions that exhibits unconventional superconductivity (beyond BCS theory). The model resembles an idealized conductor-dielectric-conductor trilayer. The Cooper pair consists of electrons on opposite sides of the dielectric, which mediates the attraction. In the strong coupling limit, we use degenerate perturbation theory to show that the model reduces to a superconducting hard-core Bose-Hu…
"Spin-Disentangled" Exact Diagonalization of Repulsive Hubbard Systems: Superconducting Pair Propagation
通过一种新的精确对角化技术，我们表明，束缚对之间的排斥哈伯德集群在超导的方式传播。必须处理的矩阵的大小取决于费米子组态的数量{ \em per spin}，其数量级为希尔伯特空间总大小的平方根。我们使用由弱O-O键连接的CuO $_{4}$单元来模拟铜氧化物中的面间耦合和c轴超导电性。Cu $_{2}$ O $_{8}$和Cu $_{3}$ O $_{12}$的数值结果提示了一种新的描述束缚对传播和三维几何中超导磁通量子化的解析方案。
We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulo…
We have rigorously shown that a strong Hubbard repulsion can cause superconductivity. The model, which has a particular set of local symmetries, manifests the phase diagram of many unconventional superconductors; anti-ferromagnetism paramagnetism, superconductivity, and even ferromagnetism are all observed. The key technique in the analysis is an exact non-linear fermion transformation, which preserves the correlated motion of electrons while removing the strong interactions. Using resolvent formalism, it is exactly shown that two holes at the Mott point bind to form a localised Cooper pair. A…
