哈里斯準則對淬火無序二維量子自旋系統的有效性
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2020
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Inspired by many evidence showing that the Harris criterion could be violated in quantum phase transitions, we study the second-order quantum phase transition of a spin-1/2 antiferromagnetic Heisenberg model with a specific quenched disorder. In particular, various strengths of randomness are considered in our investigation. The studied models will undergo quantum phase transitions by tuning the dimerized-couplings which are close related to the strength of randomness. In addition, the strength of the employed randomness is controlled by a parameter $p$ which is in the range from 0 to 1, where the clean model corresponds to $p=0$. In this study, we use the stochastic series expansion with efficient loop-update to perform the large-scale quantum Monte Carlo simulation and compute certain physical observables of the model. The critical exponent of the correlation length is evaluated from the finite-size scaling analysis with the Binder ratios as the observables. In order to estimate the statistical uncertainties in a self-consistent way, we analyze the data in the Bayesian inference framework. In the case of $p=0$, we find that the critical exponent of the correlation length $\nu$ is 0.702(9) which is in reasonably good agreement with the result of $\mathcal{O}(3)$ universality class, and doesn't fulfill the Harris inequality $\nu>2/d$, where $d$ is the spatial dimension and is 2 in this case. Remarkably, while we find that those $\nu$ of $p \le 0.8$ do not fulfill the Harris inequality $\nu > 2/d$, the $\nu$ associated with $p = 0.9$ satisfies such. This interesting phenomenon is not pointed out explicitly before in the literature.
Inspired by many evidence showing that the Harris criterion could be violated in quantum phase transitions, we study the second-order quantum phase transition of a spin-1/2 antiferromagnetic Heisenberg model with a specific quenched disorder. In particular, various strengths of randomness are considered in our investigation. The studied models will undergo quantum phase transitions by tuning the dimerized-couplings which are close related to the strength of randomness. In addition, the strength of the employed randomness is controlled by a parameter $p$ which is in the range from 0 to 1, where the clean model corresponds to $p=0$. In this study, we use the stochastic series expansion with efficient loop-update to perform the large-scale quantum Monte Carlo simulation and compute certain physical observables of the model. The critical exponent of the correlation length is evaluated from the finite-size scaling analysis with the Binder ratios as the observables. In order to estimate the statistical uncertainties in a self-consistent way, we analyze the data in the Bayesian inference framework. In the case of $p=0$, we find that the critical exponent of the correlation length $\nu$ is 0.702(9) which is in reasonably good agreement with the result of $\mathcal{O}(3)$ universality class, and doesn't fulfill the Harris inequality $\nu>2/d$, where $d$ is the spatial dimension and is 2 in this case. Remarkably, while we find that those $\nu$ of $p \le 0.8$ do not fulfill the Harris inequality $\nu > 2/d$, the $\nu$ associated with $p = 0.9$ satisfies such. This interesting phenomenon is not pointed out explicitly before in the literature.
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none, quantum phase transition, quenched disorder, Harris criterion, quantum Monte Carlo