We study the competition between stripe states with different periods and a uniform $d$ -wave superconducting state in the extended two-dimensional Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping ${t}^{\ensuremath{'}}$, the preferred period of the stripe decreases. For the values of ${t}^{\ensuremath{'}}$ predicted for cuprate high- ${T}_{c}$ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at $1/8$ doping. Only at larger doping, $0.18\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, the period 4 stripe exhibits coexisting $d$ -wave superconducting order. The uniform $d$ -wave state is only favored for sufficiently large positive ${t}^{\ensuremath{'}}$.We study the competition between stripe states with different periods and a uniform $d$-wave superconducting state in the extended two-dimensional Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping ${t}^{\ensuremath{'}}$, the preferred period of the stripe decreases. For the values of ${t}^{\ensuremath{'}}$ predicted for cuprate high-${T}_{c}$ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at $1/8$ doping. Only at larger doping, $0.18\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, the period 4 stripe exhibits coexisting $d$-wave superconducting order. The uniform $d$-wave state is only favored for sufficiently large positive ${t}^{\ensuremath{'}}$.

arXiv:1907.01909Physical review. B./Physical review. BNov 25, 201987 citations

Enhancement of superconductivity in a striped 2D Hubbard model

Thomas Maier, Gonzalo A. Álvarez, Michael S. Summers +1 more

Bulletin of the American Physical SocietyDec 10, 20090 citations

Coexistence of superconductivity with partially filled stripes in the Hubbard model

Hao Xu, Chia-Min Chung, Mingpu Qin +3 more

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.

arXiv:2303.08376ScienceMay 9, 2024144 citations

Extreme competition between stripes and superconductivity in the hole-doped Hubbard model

Ao Chen, Johnnie Gray, Si-Jing Du +1 more

The two-dimensional Hubbard model was originally proposed as the minimal model of uniform $d$ -wave superconductivity in the cuprate high-temperature superconductors, but recent calculations with relevant parameters in a realistic doping regime have often found other ground states. Further, uncertainty remains over such results due to the intrinsic bias of different computational methods. Here we address this uncertainty through state-of-the-art neural tensor network and neural backflow state simulations, enabled by large-scale GPU computation, that together reach an unprecedented variational accuracy on lattices with up to 1024 sites. At $1/8$ doping in the pure Hubbard model, as well as with next-nearest-neighbor hopping relevant to the hole-doped cuprates, we reveal a near degeneracy among a low-energy uniform $d$ -wave state, superconducting stripes, and non-superconducting stripe states on the milli- $t$ energy scale. Our work rebalances the narrative that the Hubbard model supports a single dominant order in relevant parameter regimes towards a picture of extreme competition between stripes and superconductivity.The two-dimensional Hubbard model was originally proposed as the minimal model of uniform $d$-wave superconductivity in the cuprate high-temperature superconductors, but recent calculations with relevant parameters in a realistic doping regime have often found other ground states. Further, uncertainty remains over such results due to the intrinsic bias of different computational methods. Here we address this uncertainty through state-of-the-art neural tensor network and neural backflow state simulations, enabled by large-scale GPU computation, that together reach an unprecedented variational accuracy on lattices with up to 1024 sites. At $1/8$ doping in the pure Hubbard model, as well as with next-nearest-neighbor hopping relevant to the hole-doped cuprates, we reveal a near degeneracy among a low-energy uniform $d$-wave state, superconducting stripes, and non-superconducting stripe states on the milli-$t$ energy scale. Our work rebalances the narrative that the Hubbard model supports a single dominant order in relevant parameter regimes towards a picture of extreme competition between stripes and superconductivity.

cond-mat.str-elCross-listedarXiv:2610.30321Oct 23, 20260 citations

Superconducting stripes in the hole-doped three-band Hubbard model

Boris Ponsioen, Sangwoo S. Chung, Philippe Corboz

We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale two-dimensional tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $\ensuremath{\delta}\ensuremath{\sim}0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting $d$ -wave superconductivity in the doping range $0.15\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, while at smaller doping around $\ensuremath{\delta}\ensuremath{\sim}1/8$ we find a strong competition between superconducting and nonsuperconducting stripes, including also pair density-wave states with an alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale two-dimensional tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $\ensuremath{\delta}\ensuremath{\sim}0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting $d$-wave superconductivity in the doping range $0.15\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, while at smaller doping around $\ensuremath{\delta}\ensuremath{\sim}1/8$ we find a strong competition between superconducting and nonsuperconducting stripes, including also pair density-wave states with an alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.

arXiv:2306.12910Physical review. B./Physical review. BNov 27, 202328 citations

We study the competition between stripe states with different periods and a uniform

d

-wave superconducting state in the extended two-dimensional Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping ${t}^{\ensuremath{'}}$, the preferred period of the stripe decreases. For the values of ${t}^{\ensuremath{'}}$ predicted for cuprate high-

{T}_{c}

superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at

1/8

doping. Only at larger doping, $0.18\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, the period 4 stripe exhibits coexisting

d

-wave superconducting order. The uniform

d

-wave state is only favored for sufficiently large positive ${t}^{\ensuremath{'}}$.

The two-dimensional Hubbard model was originally proposed as the minimal model of uniform

d

-wave superconductivity in the cuprate high-temperature superconductors, but recent calculations with relevant parameters in a realistic doping regime have often found other ground states. Further, uncertainty remains over such results due to the intrinsic bias of different computational methods. Here we address this uncertainty through state-of-the-art neural tensor network and neural backflow state simulations, enabled by large-scale GPU computation, that together reach an unprecedented variational accuracy on lattices with up to 1024 sites. At

1/8

doping in the pure Hubbard model, as well as with next-nearest-neighbor hopping relevant to the hole-doped cuprates, we reveal a near degeneracy among a low-energy uniform

d

-wave state, superconducting stripes, and non-superconducting stripe states on the milli-

t

energy scale. Our work rebalances the narrative that the Hubbard model supports a single dominant order in relevant parameter regimes towards a picture of extreme competition between stripes and superconductivity.

d

-wave superconductivity in the doping range $0.15\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, while at smaller doping around $\ensuremath{\delta}\ensuremath{\sim}1/8$ we find a strong competition between superconducting and nonsuperconducting stripes, including also pair density-wave states with an alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.