BMN Spread Complexity Across Phase Transitions
Abstract
We investigate the dynamical behavior and spread complexity of quantum states within the mass-deformed BMN matrix model equipped with an emergent U(1) global charge at finite temperature β−1 and chemical potential ν. Focusing on the strong-coupling regime (μ≫ 1), we model the dynamics via a charged Thermofield Double (cTFD) state and trace the evolution of spread complexity across three distinct thermodynamic regimes. In the low-temperature gapped phase (βμ≫ 1), discrete mass-gap bound states dominate, trapping wavepacket dispersion and producing non-chaotic, oscillatory early-time growth. Conversely, in the high-temperature continuum phase (βμ≪ 1), thermal excitations overwhelm the mass gap, driving a transition to a continuous advection field that exhibits maximal chaotic scrambling with a Krylov Lyapunov exponent λK = π/ β that saturates the universal bound. In the intermediate temperature regime (βμ∼ 1, βν∼ 1), the interplay between mass-gap bound states and the continuous thermal background induces a sub-leading correction to the Lanczos coefficients bn ∼ π/β n + γ√n, governing a continuous sub-exponential crossover before full chaotic thermalization. Technical derivations regarding KMS boundary conditions, grand canonical spectral moments, residue analysis, and time-reversal symmetry breaking in Krylov space are detailed in four dedicated appendices.
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BibTeX
@misc{roychowdhury2026spread,
title = {{BMN Spread Complexity Across Phase Transitions}},
author = {Dibakar Roychowdhury},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29816},
eprint = {2608.29816},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29816},
}
RIS
TY - UNPB
TI - BMN Spread Complexity Across Phase Transitions
AU - Dibakar Roychowdhury
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29816
UR - https://arxiv.org/abs/2608.29816
AB - We investigate the dynamical behavior and spread complexity of quantum states within the mass-deformed BMN matrix model equipped with an emergent U(1) global charge at finite temperature β^−1 and chemical potential ν. Focusing on the strong-coupling regime (μ≫ 1), we model the dynamics via a charged Thermofield Double (cTFD) state and trace the evolution of spread complexity across three distinct thermodynamic regimes. In the low-temperature gapped phase (βμ≫ 1), discrete mass-gap bound states dominate, trapping wavepacket dispersion and producing non-chaotic, oscillatory early-time growth. Conversely, in the high-temperature continuum phase (βμ≪ 1), thermal excitations overwhelm the mass gap, driving a transition to a continuous advection field that exhibits maximal chaotic scrambling with a Krylov Lyapunov exponent λ_K = π/ β that saturates the universal bound. In the intermediate temperature regime (βμ∼ 1, βν∼ 1), the interplay between mass-gap bound states and the continuous thermal background induces a sub-leading correction to the Lanczos coefficients b_n ∼ π/β n + γ√n, governing a continuous sub-exponential crossover before full chaotic thermalization. Technical derivations regarding KMS boundary conditions, grand canonical spectral moments, residue analysis, and time-reversal symmetry breaking in Krylov space are detailed in four dedicated appendices.
ER -