Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the $t$-$t^\prime$ Hubbard Model
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arXiv
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| Format: | Preprint |
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2026
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| author | Li, Qiaoyi Qi, Yang Li, Wei |
| author_facet | Li, Qiaoyi Qi, Yang Li, Wei |
| contents | The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-$T_c$ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the $t$-$t^\prime$ Hubbard model. On the electron-doped side, we find a $d$-wave superconducting (dSC) regime, supporting the scenario of high-$T_c$ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near $(0, π)$, distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-$T_c$ superconductors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16293 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the $t$-$t^\prime$ Hubbard Model Li, Qiaoyi Qi, Yang Li, Wei Strongly Correlated Electrons Superconductivity The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-$T_c$ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the $t$-$t^\prime$ Hubbard model. On the electron-doped side, we find a $d$-wave superconducting (dSC) regime, supporting the scenario of high-$T_c$ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near $(0, π)$, distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-$T_c$ superconductors. |
| title | Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the $t$-$t^\prime$ Hubbard Model |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2604.16293 |