Driven Critical Dynamics in Measurement-induced Phase Transitions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909383331414016 |
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| author | Wang, Wantao Liu, Shuo Li, Jiaqiang Zhang, Shi-Xin Yin, Shuai |
| author_facet | Wang, Wantao Liu, Shuo Li, Jiaqiang Zhang, Shi-Xin Yin, Shuai |
| contents | Measurement-induced phase transitions (MIPT), characterizing abrupt changes in entanglement properties in quantum many-body systems subjected to unitary evolution with interspersed projective measurements, have garnered increasing interest. In this work, we generalize the Kibble-Zurek (KZ) driven critical dynamics that has achieved great success in traditional quantum and classical phase transitions to MIPT. By linearly changing the measurement probability $p$ to cross the critical point $p_c$ with driving velocity $R$, we identify the dynamic scaling relation of the entanglement entropy $S$ versus $R$ at $p_c$. For decreasing $p$ from the area-law phase, $S$ satisfies $S\propto \ln R$; while for increasing $p$ from the volume-law phase, $S$ satisfies $S\propto R^{1/r}$ in which $r=z+1/ν$ with $z$ and $ν$ being the dynamic and correlation length exponents, respectively. Moreover, we find that the driven dynamics from the volume-law phase violates the adiabatic-impulse scenario of the KZ mechanism. In spite of this, a unified finite-time scaling (FTS) form can be developed to describe these scaling behaviors. Besides, the dynamic scaling of the entanglement entropy of an auxiliary qubit $S_Q$ is also investigated to further confirm the universality of the FTS form. By successfully establishing the driven dynamic scaling theory of this newfashioned entanglement transition, we bring a new fundamental perspective into MIPT that can be detected in fast-developing quantum computers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Driven Critical Dynamics in Measurement-induced Phase Transitions Wang, Wantao Liu, Shuo Li, Jiaqiang Zhang, Shi-Xin Yin, Shuai Quantum Physics Statistical Mechanics Strongly Correlated Electrons Measurement-induced phase transitions (MIPT), characterizing abrupt changes in entanglement properties in quantum many-body systems subjected to unitary evolution with interspersed projective measurements, have garnered increasing interest. In this work, we generalize the Kibble-Zurek (KZ) driven critical dynamics that has achieved great success in traditional quantum and classical phase transitions to MIPT. By linearly changing the measurement probability $p$ to cross the critical point $p_c$ with driving velocity $R$, we identify the dynamic scaling relation of the entanglement entropy $S$ versus $R$ at $p_c$. For decreasing $p$ from the area-law phase, $S$ satisfies $S\propto \ln R$; while for increasing $p$ from the volume-law phase, $S$ satisfies $S\propto R^{1/r}$ in which $r=z+1/ν$ with $z$ and $ν$ being the dynamic and correlation length exponents, respectively. Moreover, we find that the driven dynamics from the volume-law phase violates the adiabatic-impulse scenario of the KZ mechanism. In spite of this, a unified finite-time scaling (FTS) form can be developed to describe these scaling behaviors. Besides, the dynamic scaling of the entanglement entropy of an auxiliary qubit $S_Q$ is also investigated to further confirm the universality of the FTS form. By successfully establishing the driven dynamic scaling theory of this newfashioned entanglement transition, we bring a new fundamental perspective into MIPT that can be detected in fast-developing quantum computers. |
| title | Driven Critical Dynamics in Measurement-induced Phase Transitions |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.06648 |