We investigate the interplay between charge order and superconductivity near an antiferromagnetic quantum critical point using sign-problem-free Quantum Monte Carlo simulations. We establish that, when the electronic dispersion is particle-hole symmetric, the system has an emergent SU(2) symmetry that implies a degeneracy between $d$-wave superconductivity and charge order with $d$-wave form factor. Deviations from particle-hole symmetry, however, rapidly lift this degeneracy, despite the fact that the SU(2) symmetry is preserved at low energies. As a result, we find a strong suppression of charge order caused by the competing, leading superconducting instability. Across the antiferromagnetic phase transition, we also observe a shift in the charge order wave vector from diagonal to axial. We discuss the implications of our results to the universal phase diagram of antiferromagnetic quantum-critical metals and to the elucidation of the charge order experimentally observed in the cuprates.

中文翻译：

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反铁磁量子临界点附近电荷阶的易碎性

我们使用无符号问题的量子蒙特卡洛模拟研究了反铁磁量子临界点附近电荷序与超导之间的相互作用。我们确定，当电子弥散是粒子-孔对称时，系统具有SU（2）对称性，这意味着$d$波超导和带电顺序 $d$波形系数。尽管SU（2）对称性保持在低能量下，但与粒子-孔对称性的偏差迅速消除了这种简并性。结果，我们发现由竞争导致的超导不稳定性引起的电荷顺序的强烈抑制。跨反铁磁相变，我们还观察到电荷阶波矢量从对角线到轴向的位移。我们讨论了我们的结果对反铁磁量子临界金属的通用相图的影响，以及对在铜酸盐中实验观察到的电荷顺序的阐明的含义。