V2EX density matrix renormalization group

Density Matrix Renormalization Group

释义 Definition

密度矩阵重整化群(DMRG):一种用于求解强关联量子多体系统(尤其是一维量子链)基态与低能激发的高精度数值方法。它通过保留“最重要”的量子态(由约化密度矩阵的本征值衡量)来有效截断希尔伯特空间,从而显著降低计算复杂度。常见于凝聚态物理与量子化学的张量网络(如 MPS)框架中。

发音 Pronunciation (IPA)

/dn.s.ti me.trks rnr.m.laze.n rup/

例句 Examples

DMRG is widely used to study one-dimensional quantum spin chains.
DMRG 常用于研究一维量子自旋链。

By combining symmetry constraints with the density matrix renormalization group, the researchers obtained highly accurate ground-state energies for a strongly correlated model.
通过将对称性约束与密度矩阵重整化群结合,研究人员为一个强关联模型得到了高精度的基态能量。

词源 Etymology

该术语由三部分组成:density matrix(密度矩阵) + renormalization(重整化) + group(群/方法框架)。它强调方法的核心思想:用系统某部分的约化密度矩阵来判断哪些态对整体物理最重要,并在“重整化”的迭代过程中保留这些态。DMRG 由物理学家 Steven R. White 在 1990 年代提出并发展,后来与矩阵乘积态(MPS)等张量网络语言逐渐统一。

相关词 Related Words

文学与著作 Literary Works

  • Steven R. White, “Density matrix formulation for quantum renormalization groups”, Physical Review Letters (1992)
  • Steven R. White, “Density-matrix algorithms for quantum renormalization groups”, Physical Review B (1993)
  • Ulrich Schollwck, “The density-matrix renormalization group”, Reviews of Modern Physics (2005)
  • Ulrich Schollwck, “The density-matrix renormalization group in the age of matrix product states”, Annals of Physics (2011)
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