DMRG Parameters
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DMRG Algorithm
White (1992, 1993): DMRG keeps the χ most relevant eigenstates of the reduced density matrix ρ = Tr_env|Ψ⟩⟨Ψ|.
Sweep procedure:
• Left-to-right: optimize A[1],A[2],...,A[L-1]
• Right-to-left: optimize A[L-1],...,A[1]
• Each step: 2-site effective Hamiltonian in χ² × d² space, Lanczos to find ground state, SVD to update bond tensor.
Truncation error: ε = 1 - Σᵢ₌₁^χ λᵢ² controls accuracy. Gapped phases: ε ~ e^{-χ}. Critical: ε ~ χ^{-κ}.
MBL: With disorder W, entanglement follows area law even for excited states → DMRG works well in MBL phase.
Sweep procedure:
• Left-to-right: optimize A[1],A[2],...,A[L-1]
• Right-to-left: optimize A[L-1],...,A[1]
• Each step: 2-site effective Hamiltonian in χ² × d² space, Lanczos to find ground state, SVD to update bond tensor.
Truncation error: ε = 1 - Σᵢ₌₁^χ λᵢ² controls accuracy. Gapped phases: ε ~ e^{-χ}. Critical: ε ~ χ^{-κ}.
MBL: With disorder W, entanglement follows area law even for excited states → DMRG works well in MBL phase.