We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like s...We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like stochastic gradient(SG)met hods,the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function,our method can be easily implemented.Theoretical and computational properties of SMBA are studied,and convergence results are established.Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm(MBA)for the structure of our problem.展开更多
Understanding the interplay between screening,electronic correlations,and collective excitations is essential for the design of two-dimensional quantum materials.Here,we present a comprehensive first-principles study ...Understanding the interplay between screening,electronic correlations,and collective excitations is essential for the design of two-dimensional quantum materials.Here,we present a comprehensive first-principles study of more than 60 MA_(2)Z_(4)monolayers,encompassing semiconducting,metallic,cold-metallic,magnetic,and topological phases.Using the constrained random phase approximation(cRPA),wecompute material-specific effectiveCoulomb interaction parametersU,U0,and J,including their spatial dependence across distinct correlated subspaces defined by local coordination and crystal symmetry.In semiconducting compounds,long-range nonlocal interactions persist,revealing unconventional screening and suggesting strong excitonic effects beyond simple dielectricmodels.In cold-metallic systems,sizable long-range Coulomb interactions remain despite the presence of free carriers,highlighting their atypical metallic screening.Among 33-valence-electron compounds,we find U^(eff)>W in theβ2 phase,indicating proximity to charge-density-wave or Mott instabilities.Several V-and Nb-based systems exhibit intermediate-to-strong correlation strength,with U/W>1 in multiple cases.Using cRPA-derived Stoner parameters,we identify magnetic instabilities in various V-,Nb-,Cr-,andMn-based compounds.Finally,selected cold-metallic systems display plasmon dispersions that deviate from the conventional√q behavior,revealing nearly non-dispersive low-energy modes.These results position MA_(2)Z_(4)monolayers as a versatile platform for investigating correlation-driven instabilities and emergent collective behavior in two dimensions.展开更多
文摘We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like stochastic gradient(SG)met hods,the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function,our method can be easily implemented.Theoretical and computational properties of SMBA are studied,and convergence results are established.Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm(MBA)for the structure of our problem.
基金supported by the Iran National Science Foundation(INSF)under Project No.4044100the Collaborative Research Center CRC/TRR 227 of the Deutsche Forschungsgemeinschaft(DFG),and the European Union(EFRE)via Grant No.ZS/2016/06/79307.
文摘Understanding the interplay between screening,electronic correlations,and collective excitations is essential for the design of two-dimensional quantum materials.Here,we present a comprehensive first-principles study of more than 60 MA_(2)Z_(4)monolayers,encompassing semiconducting,metallic,cold-metallic,magnetic,and topological phases.Using the constrained random phase approximation(cRPA),wecompute material-specific effectiveCoulomb interaction parametersU,U0,and J,including their spatial dependence across distinct correlated subspaces defined by local coordination and crystal symmetry.In semiconducting compounds,long-range nonlocal interactions persist,revealing unconventional screening and suggesting strong excitonic effects beyond simple dielectricmodels.In cold-metallic systems,sizable long-range Coulomb interactions remain despite the presence of free carriers,highlighting their atypical metallic screening.Among 33-valence-electron compounds,we find U^(eff)>W in theβ2 phase,indicating proximity to charge-density-wave or Mott instabilities.Several V-and Nb-based systems exhibit intermediate-to-strong correlation strength,with U/W>1 in multiple cases.Using cRPA-derived Stoner parameters,we identify magnetic instabilities in various V-,Nb-,Cr-,andMn-based compounds.Finally,selected cold-metallic systems display plasmon dispersions that deviate from the conventional√q behavior,revealing nearly non-dispersive low-energy modes.These results position MA_(2)Z_(4)monolayers as a versatile platform for investigating correlation-driven instabilities and emergent collective behavior in two dimensions.
