| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Imaginary-Time Quantum Relaxation Critical Dynamics with Semi-Ordered Initial States |
| Zhi-Xuan Li1, Shuai Yin2, and Yu-Rong Shu1* |
1School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China
2School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
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| Cite this article: |
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Zhi-Xuan Li, Shuai Yin, and Yu-Rong Shu 2023 Chin. Phys. Lett. 40 037501 |
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Abstract We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial states, in which the order parameter $M$ decays homogeneously as $M\propto \tau^{-\beta/\nu z}$, here $M$ depends on the location $x$, showing rich scaling behaviors. Similar to the classical relaxation dynamics with an initial domain wall in model A, which describes the purely dissipative dynamics, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as $M\propto \tau^{-\beta_1/\nu z}$, with $\beta_1$ being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as $M\propto \tau^{-\beta/\nu z}$ in the short-time stage, then crosses over to the scaling behavior of $M\propto \tau^{-\beta_1/\nu z}$ when the location $x$ is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and $\beta_1$ is not an independent exponent.
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Received: 22 December 2022
Published: 18 February 2023
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| PACS: |
75.40.Gb
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(Dynamic properties?)
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64.60.Ht
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(Dynamic critical phenomena)
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68.35.Rh
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(Phase transitions and critical phenomena)
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75.10.Jm
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(Quantized spin models, including quantum spin frustration)
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