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Glasses show vibrational and mechanical properties that are markedly different from other crystalline materials [@Phillips_1981; @Alexander_1998]. Thermal measurements and scattering experiments have been performed to study the properties of various glassy systems, such as covalent-bonding [@Zeller_1971; @Buchenau_1984; @Nakayama_2002; @Monaco_2006; @Baldi_2010; @Chumakov_2011], molecular [@Yamamuro_1996; @Ramos_2003; @Monaco_2009; @Shibata_2015; @Kabeya_2016], metallic [@Berg_1983; @Yong_2008; @Bruna_2011; @Huang_2014], and polymeric [@Niss_2007; @Hong_2008; @Caponi_2011; @Perez-Castaneda2_2014; @Terao_2018; @Zorn_2018] glasses. For instance, the excess vibrational modes at low frequencies and the excess heat capacity at low temperatures exceeding the Debye predictions, which describe the corresponding crystalline values, have been observed universally in various glassy materials. This phenomenon, which is referred to as the boson peak (BP), has been widely studied.

The ideas of elastic heterogeneities [@Schirmacher_2006; @Schirmacher_2007; @Schirmacher_2015] and criticality near isostatic state and marginally stable state [@Wyart_2005; @Wyart_2006; @Wyart_2010; @DeGiuli_2014] have been introduced, following the recent theoretical advances for understanding the origin of anomalies in glasses. Based on these theories, the mean-field formulations have been developed by using the effective medium technique [@Schirmacher_2006; @Schirmacher_2007; @Schirmacher_2015; @Wyart_2010; @DeGiuli_2014]. In addition, more recent studies [@Milkus_2016; @Krausser_2017] have focused on the local inversion-symmetry breaking, which can explain the microscopic origin of the BP.

Molecular dynamics (MD) simulations play an essential 