Adiabatic Variational Principle: Born-Oppenheimer Theory for Emergent Electronic-Order Dynamics
Abstract
Recent advances in microscopic many-body methods have enabled increasingly accurate descriptions of equilibrium quantum states, yet large-scale simulations of emergent-order dynamics typically rely on phenomenological equations with prescribed free-energy functionals. We introduce the Adiabatic Variational Principle (AVP), a framework for deriving order-parameter dynamics directly from an interacting many-body Hamiltonian. When microscopic relaxation is fast compared with order-parameter evolution, the many-body state follows the collective configuration adiabatically, in analogy with the Born--Oppenheimer separation of electronic and nuclear motion. This assumption makes explicit the adiabatic closure implicit in conventional phase-field descriptions. Each instantaneous order-parameter configuration then defines a constrained quasi-stationary many-body state, and the Lagrange multipliers enforcing these constraints directly provide the thermodynamic forces driving the collective evolution. Nonlinear Mori--Zwanzig projection theory further connects the reversible dynamics to the microscopic algebra of the collective variables and relates dissipation and fluctuations to the eliminated degrees of freedom. Applications to charge- and spin-density-wave dynamics recover Allen--Cahn domain growth, resolve evolving domain networks together with their microscopic electronic structure, and yield generalized Landau--Lifshitz dynamics for itinerant magnetism. The AVP thus provides a solver-independent microscopic foundation for phase-field-like simulations of the nonequilibrium dynamics of emergent electronic order.
Related
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- Emergent Electronic Bond-Order Wave in a Quasi-One-Dimensional Chain
BibTeX
@misc{yang2026adiabatic,
title = {{Adiabatic Variational Principle: Born-Oppenheimer Theory for Emergent Electronic-Order Dynamics}},
author = {Yang Yang and Ali Rayat and Ho Jang and Yunhao Fan and Sankha Subhra Bakshi and Gia-Wei Chern},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40117},
eprint = {2610.40117},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40117},
}
RIS
TY - UNPB
TI - Adiabatic Variational Principle: Born-Oppenheimer Theory for Emergent Electronic-Order Dynamics
AU - Yang Yang
AU - Ali Rayat
AU - Ho Jang
AU - Yunhao Fan
AU - Sankha Subhra Bakshi
AU - Gia-Wei Chern
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40117
UR - https://arxiv.org/abs/2610.40117
AB - Recent advances in microscopic many-body methods have enabled increasingly accurate descriptions of equilibrium quantum states, yet large-scale simulations of emergent-order dynamics typically rely on phenomenological equations with prescribed free-energy functionals. We introduce the Adiabatic Variational Principle (AVP), a framework for deriving order-parameter dynamics directly from an interacting many-body Hamiltonian. When microscopic relaxation is fast compared with order-parameter evolution, the many-body state follows the collective configuration adiabatically, in analogy with the Born--Oppenheimer separation of electronic and nuclear motion. This assumption makes explicit the adiabatic closure implicit in conventional phase-field descriptions. Each instantaneous order-parameter configuration then defines a constrained quasi-stationary many-body state, and the Lagrange multipliers enforcing these constraints directly provide the thermodynamic forces driving the collective evolution. Nonlinear Mori--Zwanzig projection theory further connects the reversible dynamics to the microscopic algebra of the collective variables and relates dissipation and fluctuations to the eliminated degrees of freedom. Applications to charge- and spin-density-wave dynamics recover Allen--Cahn domain growth, resolve evolving domain networks together with their microscopic electronic structure, and yield generalized Landau--Lifshitz dynamics for itinerant magnetism. The AVP thus provides a solver-independent microscopic foundation for phase-field-like simulations of the nonequilibrium dynamics of emergent electronic order.
ER -