Read the equation
The spectral summary sets its middle value to zero unconditionally. No eigensolver or symmetry proof establishes an exact zero eigenvalue of the full constructed matrix. The name Goldstone mode is therefore a source interpretation that is not justified by this assignment alone.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| lambda_22 | Assigned middle spectral value |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
SpectralSummary spectral_summary() const {
SpectralSummary s;
// λ₁ = -4α - κ - γ - γ₀ (lowest, antibonding)
s.lambda_1 = -4.0 * params_.alpha - params_.kappa_intra -
params_.gamma - params_.gamma_0;
// λ₂₂ = 0 (zero mode, Goldstone)
s.lambda_22 = 0.0;
// λ₄₄ = κ + 1.2β₀ + γ + 2.618η (highest, bonding)
s.lambda_44 = params_.kappa_intra + 1.2 * params_.beta_0 +
params_.gamma + 2.618 * params_.eta;
// W = λ₄₄ - λ₁ = 4α + 2κ + 1.2β₀ + 2γ + γ₀ + 3.236η
s.spectral_width = s.lambda_44 - s.lambda_1;
return s;Exact original notation
λ₂₂ = 0 (zero mode, Goldstone)