SIM-GRAPH: A universal guide to symmetric interactions
Abstract
Symmetry plays a central role throughout physics, from Fourier analysis on discrete lattices to the classification of elementary particles in the standard model. In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries. Here, we present the SIM-GRAPH method (Symmetric Ising Models - Graph Reduction And Projected Hamiltonians), which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems. By projecting all interactions onto a symmetric subset of the system, the method effectively reduces the number of sites, thus providing an exponential speedup over standard exact diagonalization. Furthermore, we introduce two extensions that broaden the applicability of the method and allow for a controlled trade-off between computational cost and accuracy.
Related
- An obstruction to cosmic acceleration from shift-symmetric dark sector interactions
- Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions
- Universal orbital-coupling rules for hydrogen-defect interactions in bcc metals
- Extended symmetric quantum phase in a honeycomb Heisenberg model with sublattice-selective interactions
- Universal dynamics of quantum phase transitions with fractional long-range interactions
BibTeX
@misc{verstraten2026simgraph,
title = {{SIM-GRAPH: A universal guide to symmetric interactions}},
author = {R. C. Verstraten and C. Morais Smith},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09996},
eprint = {2609.09996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09996},
}
RIS
TY - UNPB
TI - SIM-GRAPH: A universal guide to symmetric interactions
AU - R. C. Verstraten
AU - C. Morais Smith
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09996
UR - https://arxiv.org/abs/2609.09996
AB - Symmetry plays a central role throughout physics, from Fourier analysis on discrete lattices to the classification of elementary particles in the standard model. In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries. Here, we present the SIM-GRAPH method (Symmetric Ising Models - Graph Reduction And Projected Hamiltonians), which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems. By projecting all interactions onto a symmetric subset of the system, the method effectively reduces the number of sites, thus providing an exponential speedup over standard exact diagonalization. Furthermore, we introduce two extensions that broaden the applicability of the method and allow for a controlled trade-off between computational cost and accuracy.
ER -