Hidden Gauge Freedom in Complex-Pole Hierarchical Equations of Motion

• URL: http://arxiv.org/abs/2607.04834v1
• Date: Mon, 06 Jul 2026 09:08:52 GMT
• Title: Hidden Gauge Freedom in Complex-Pole Hierarchical Equations of Motion
• Abstract summary: We report a previously unknown gauge freedom in complex-pole HEOM.<n>This gauge controls both the eigenspectrum and non-normality of the hierarchy generator.<n>We extend numerically exact simulations of sub-Ohmic dynamics to previously inaccessible coupling strengths.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While complex-pole hierarchical equations of motion (HEOM) have dramatically expanded the reach of numerically exact quantum dynamics simulations of open quantum systems, they suffer from numerical instabilities rooted in the non-Hermitian structure of their Liouvillian. Yet, the origin of this structure remains obscure. Here, we report a previously unknown gauge freedom in complex-pole HEOM: a continuous family of analytically equivalent Liouvillians, all encoding the same bath correlation function, whose numerical properties vary dramatically. This gauge controls both the eigenspectrum and non-normality of the hierarchy generator, revealing spectral divergence and non-normal error amplification as two distinct instability mechanisms. By optimizing this gauge, we introduce GO--HEOM, which eliminates divergences in strongly coupled Brownian oscillator environments and extends numerically exact simulations of sub-Ohmic dynamics -- including through the delocalized-to-localized quantum phase transition -- to previously inaccessible coupling strengths. Because this gauge transformation is independent of the bath-correlation decomposition scheme, our GO--HEOM becomes a general, broadly compatible strategy for accessing numerically exact quantum dynamics of open quantum systems over arbitrary coupling and highly non-Markovian regimes.

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