Sign structure of the $t$-$t^\prime$-$J$ model and its physical consequences
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909346962604032 |
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| author | Lu, Xin Zhang, Jia-Xin Gong, Shou-Shu Sheng, D. N. Weng, Zheng-Yu |
| author_facet | Lu, Xin Zhang, Jia-Xin Gong, Shou-Shu Sheng, D. N. Weng, Zheng-Yu |
| contents | Understanding the doped Mott insulator is a central challenge in condensed matter physics. In this work, we first explicitly identify a new sign structure in the $t$-$t'$-$J$ model on the square lattice that replaces the conventional Fermi statistics for weakly interacting electrons. Then we show that the singular, i.e., the phase-string part of the sign structure in the partition function can be precisely turned off in a modified model. The density matrix renormalization group method is then employed to study these two models comparatively on finite-size systems, which is designed to unveil the consequences of the phase-string component. We find that the hole pairing is present not only in the quasi-long-range superconducting phase but also in the stripe phase of the $t$-$t'$-$J$ model. However, once the phase-string is switched off, both the superconducting and stripe orders together with the underlying hole pairing disappear. The corresponding ground state reduces to a trivial Fermi-liquid-like state with small hole Fermi pockets that is decoupled from the antiferromagnetic spin background. It is in sharp contrast to the original $t$-$t'$-$J$ model where large Fermi surfaces can be restored in the stripe phase found at $t'/t<0$ or the superconducting phase at $t'/t>0$ in the six-leg ladder calculation. Our study clearly demonstrates that the strong correlation effect in doped Mott insulator should be mainly attributed to the long-range quantum entanglement between the spin and charge, which is, non-perturbatively, beyond a simple spin-charge separation under the no double occupancy constraint. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_13498 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sign structure of the $t$-$t^\prime$-$J$ model and its physical consequences Lu, Xin Zhang, Jia-Xin Gong, Shou-Shu Sheng, D. N. Weng, Zheng-Yu Strongly Correlated Electrons Superconductivity Understanding the doped Mott insulator is a central challenge in condensed matter physics. In this work, we first explicitly identify a new sign structure in the $t$-$t'$-$J$ model on the square lattice that replaces the conventional Fermi statistics for weakly interacting electrons. Then we show that the singular, i.e., the phase-string part of the sign structure in the partition function can be precisely turned off in a modified model. The density matrix renormalization group method is then employed to study these two models comparatively on finite-size systems, which is designed to unveil the consequences of the phase-string component. We find that the hole pairing is present not only in the quasi-long-range superconducting phase but also in the stripe phase of the $t$-$t'$-$J$ model. However, once the phase-string is switched off, both the superconducting and stripe orders together with the underlying hole pairing disappear. The corresponding ground state reduces to a trivial Fermi-liquid-like state with small hole Fermi pockets that is decoupled from the antiferromagnetic spin background. It is in sharp contrast to the original $t$-$t'$-$J$ model where large Fermi surfaces can be restored in the stripe phase found at $t'/t<0$ or the superconducting phase at $t'/t>0$ in the six-leg ladder calculation. Our study clearly demonstrates that the strong correlation effect in doped Mott insulator should be mainly attributed to the long-range quantum entanglement between the spin and charge, which is, non-perturbatively, beyond a simple spin-charge separation under the no double occupancy constraint. |
| title | Sign structure of the $t$-$t^\prime$-$J$ model and its physical consequences |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2303.13498 |