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arXiv:2211.01771 · Physical review. B./Physical review. B

Competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction

Runyu Ma, Tianxing Ma

Published Jun 13, 2023• 3 citations
arXivHTMLPDF

Abstract

The competition between antiferromagnetism and superconductivity is one of the central questions in research involving strongly correlated systems. In this paper, we utilize a double-layer model containing Hubbard interaction and interlayer Heisenberg interaction to reveal their competition. This model is free of the sign problem under certain conditions, and we perform projector quantum Monte Carlo simulations to extract the ground-state correlations of magnetism and superconductivity. Our results show that the superconductivity emerges when the antiferromagnetism is suppressed by tuning the filling or the anisotropy of the interlayer Heisenberg interaction. This model can be seen as an analog of unconventional superconductors and may help us to understand the transition from an antiferromagnetic insulator to a superconductor.

DOI
10.1103/physrevb.107.214509

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The competition between antiferromagnetism and superconductivity is one of the central questions in research involving strongly correlated systems. In this paper, we utilize a double-layer model containing Hubbard interaction and interlayer Heisenberg interaction to reveal their competition. This model is free of the sign problem under certain conditions, and we perform projector quantum Monte Carlo simulations to extract the ground-state correlations of magnetism and superconductivity. Our results show that the superconductivity emerges when the antiferromagnetism is suppressed by tuning the filling or the anisotropy of the interlayer Heisenberg interaction. This model can be seen as an analog of unconventional superconductors and may help us to understand the transition from an antiferromagnetic insulator to a superconductor.
How superconductivity emerges in the vicinity of an antiferromagnetic insulating state is a long-standing issue of strong correlation physics. We study the transition from an antiferromagnetic insulator to a superconductor by hole doping based on a bilayer generalization of a Hubbard model. The projector quantum Monte Carlo simulations are employed, which are sign problem free both at and away from half filling. An anisotropic Ising antiferromagnetic Mott insulating phase occurs at half filling, which is weakened by hole doping. Below a critical doping value, antiferromagnetism coexists with the singlet superconductivity, which is a pairing across each rung with an extended sss-wave symmetry. As doping further increases, the antiferromagnetic order vanishes, leaving only a superconducting phase. These results provide important information on how superconductivity appears upon doping the parent Mott-insulating state.
Competing orders represent a central challenge in understanding strongly correlated systems. In this work, we employ projector quantum Monte Carlo simulations to study a sign-problem-free bilayer extended Hubbard model. In this model, a charge stripe phase, characterized by a peak at (0±2πδ,0) is induced by highly anisotropic interlayer antiferromagnetic spin-exchange coupling Jz, and strongly suppressed by the decreasing spin-exchange anisotropy (i.e., introducing the spin-flip term J⊥); in contrast, the introduction of J⊥ favors the emergence of interlayer pairing superconductivity. We further demonstrate that the anisotropy of the interlayer spin-exchange directly governs the competition between these two phases, while the on-site interaction U plays a complex role in tuning both the charge stripe and superconductivity. Furthermore, against the background of charge stripes we discover the spin stripes, characterized by twice the period of charge stripes, indicating the profound internal connection between them. Our work identifies the key factors driving charge stripe formation, highlights the sensitivity of both the charge stripe and superconducting phases to interaction parameters, and thereby provides valuable insights into competing orders in strongly correlated systems.
Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.
Unconventional superconductors such as cuprates often host competing nodal superconductivity and antiferromagnetism. These systems are typically modeled as a repulsive Hubbard model whose unbiased simulation suffers from the fermion sign-problem at any non-zero doping. Here we will exploit the fact that neither of these phases, the nodal d-wave superconductor or the antiferromagnet, require any doping for their existence, and construct a sign-problem-free repulsive Hubbard model with an additional bosonic field which hosts both of these phases. Using Quantum Monte Carlo (QMC) simulations, supplemented with mean-field theory and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the chiral Gross-Neveu-Heisenberg theory.
Cooperation and competition between the antiferromagnetic, ddd-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength UUU below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.
Using a variational Monte Carlo method, we study the competition of strong electron-electron and electron-phonon interactions in the ground state of the Holstein-Hubbard model on a square lattice. At half filling, an extended intermediate metallic or weakly superconducting (SC) phase emerges, sandwiched between antiferromagnetic and charge order (CO) insulating phases. By carrier doping into the CO insulator, the SC order dramatically increases for strong electron-phonon couplings, but is largely hampered by wide phase separation (PS) regions. Superconductivity is optimized at the border to the PS.