Efficient simulation of second-order phase transitions in quantum anharmonic materials
Abstract
When a crystal undergoes a second-order structural phase transition, such as in ferroelectrics, Peierls, and charge-density waves, the diverging fluctuations of the order parameter lead to the break- down of the standard phonon quasiparticle picture. Simulating these highly anharmonic regimes is notoriously challenging, as methods such as molecular dynamics suffer from a critical slowdown near the transition point, while the harmonic approximation fails dramatically at saddle points of the energy landscape stabilized by quantum or thermal ionic fluctuations. This work introduces a new approach, based on the variational free-energy principle, to predict critical long-range behavior and dynamical spectra in strongly anharmonic systems, even when quantum ionic fluctuations dominate. The proposed framework builds upon the stochastic self- consistent harmonic approximation but reduces its computational scaling with the number of atoms, N, from O(N^6) to O(N^2) and the memory requirement from O(N^4) to O(N). We benchmark the method on the prototypical lead-free metal-halide perovskite CsSnI3, a promising candidate for photovoltaic engineering, simulating its phase stability and Raman spectrum near the phase transition, where the breakdown of the quasiparticle picture becomes evident. We demonstrate the effectiveness of the method by computing the full free-energy Hessian and the critical temperature in a supercell with 1080 atoms. Such simulations would have required tens of thousands of years with the legacy approach; it is now feasible in a few hours on consumer hardware.
Related
- Efficient Simulation of Higher-Order Transitions in Resonance Raman Spectroscopy and Its Chiral Extension.
- A Controlled Study of Memory Hierarchy Transitions in Quantum Circuit Simulation on Apple M4 Pro Unified Memory Architecture
- Tensor Networks for Materials Simulation and Quantum Chemistry
- Measurement-efficient energy estimator for quantum chemistry of photodynamic materials
- Efficient Quantum Simulation of Linearized Vlasov--Poisson Dynamics Using Trotter and THRIFT Hamiltonian Simulation Methods
BibTeX
@misc{baldanza2026efficient,
title = {{Efficient simulation of second-order phase transitions in quantum anharmonic materials}},
author = {Andrea Baldanza and Lorenzo Monacelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.14292},
eprint = {2608.14292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.14292},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient simulation of second-order phase transitions in quantum anharmonic materials
AU - Andrea Baldanza
AU - Lorenzo Monacelli
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2608.14292
UR - https://arxiv.org/abs/2608.14292
AB - When a crystal undergoes a second-order structural phase transition, such as in ferroelectrics, Peierls, and charge-density waves, the diverging fluctuations of the order parameter lead to the break- down of the standard phonon quasiparticle picture. Simulating these highly anharmonic regimes is notoriously challenging, as methods such as molecular dynamics suffer from a critical slowdown near the transition point, while the harmonic approximation fails dramatically at saddle points of the energy landscape stabilized by quantum or thermal ionic fluctuations. This work introduces a new approach, based on the variational free-energy principle, to predict critical long-range behavior and dynamical spectra in strongly anharmonic systems, even when quantum ionic fluctuations dominate. The proposed framework builds upon the stochastic self- consistent harmonic approximation but reduces its computational scaling with the number of atoms, N, from O(N^6) to O(N^2) and the memory requirement from O(N^4) to O(N). We benchmark the method on the prototypical lead-free metal-halide perovskite CsSnI3, a promising candidate for photovoltaic engineering, simulating its phase stability and Raman spectrum near the phase transition, where the breakdown of the quasiparticle picture becomes evident. We demonstrate the effectiveness of the method by computing the full free-energy Hessian and the critical temperature in a supercell with 1080 atoms. Such simulations would have required tens of thousands of years with the legacy approach; it is now feasible in a few hours on consumer hardware.
ER -