Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915617783676928 |
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| author | Lin, He-Yu Yin, Shuai Xie, Z. Y. Lu, Zhong-Yi |
| author_facet | Lin, He-Yu Yin, Shuai Xie, Z. Y. Lu, Zhong-Yi |
| contents | We investigate the imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy. Simulating directly in the thermodynamic limit, we explore the relaxation process near the critical point with two types of initial states: a fully polarized state and a product state with a small magnetization. For the fully polarized state, the magnetization shows a power law scaling $M\propto τ^{-β/(νz)}$ in the imaginary-time evolution, from which both the critical point and critical exponent can be determined with high accuracy. For the nearly paramagnetic state, the relaxation process exhibits a behavior of $M\propto τ^θ$ with $θ=0.1958$ being the critical initial-slip exponent, which is in good agreement with that obtained from the dynamic scaling of the self-correlation in quantum Monte Carlo method. These universal features emerge well before the system converges to the ground state, demonstrating the efficiency of imaginary-time evolution for probing quantum criticality. Our results demonstrate that iPEPS can serve as a robust and scalable method for studying dynamical critical phenomena in two-dimensional quantum many-body systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_10934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states Lin, He-Yu Yin, Shuai Xie, Z. Y. Lu, Zhong-Yi Strongly Correlated Electrons Quantum Physics We investigate the imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy. Simulating directly in the thermodynamic limit, we explore the relaxation process near the critical point with two types of initial states: a fully polarized state and a product state with a small magnetization. For the fully polarized state, the magnetization shows a power law scaling $M\propto τ^{-β/(νz)}$ in the imaginary-time evolution, from which both the critical point and critical exponent can be determined with high accuracy. For the nearly paramagnetic state, the relaxation process exhibits a behavior of $M\propto τ^θ$ with $θ=0.1958$ being the critical initial-slip exponent, which is in good agreement with that obtained from the dynamic scaling of the self-correlation in quantum Monte Carlo method. These universal features emerge well before the system converges to the ground state, demonstrating the efficiency of imaginary-time evolution for probing quantum criticality. Our results demonstrate that iPEPS can serve as a robust and scalable method for studying dynamical critical phenomena in two-dimensional quantum many-body systems. |
| title | Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2511.10934 |