Topological signatures in the curvature-induced energy response
Abstract
Relativistic effective field theory predicts a topological energy response to a gravitational field that appears at third order in spatial gradients. Here, we investigate how this response emerges in the nonrelativistic Haldane model using a microscopic lattice formulation of curvature-induced deformations. We find that the leading first-order energy response is nonuniversal and depends on the bond-resolved structure of the deformation; in particular, it vanishes for a symmetric modulation of the three nearest-neighbor hoppings. At third order, the curvature-induced energy response contains a bond-symmetric component together with nonuniversal bond-dependent contributions. The bond-symmetric component, which is isolated by a uniform modulation of the three hoppings, exhibits a universal discontinuity across the topological transition whose magnitude agrees with the relativistic gravitational Chern--Simons prediction. Thus, although the full curvature-induced energy response generally contains nonuniversal lattice contributions, its third-order response retains a universal topological component beyond the relativistic limit.
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BibTeX
@misc{lee2026topological,
title = {{Topological signatures in the curvature-induced energy response}},
author = {Jaehyeok Lee and Iuegyun Hong and Jinhong Park},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28146},
eprint = {2608.28146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28146},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological signatures in the curvature-induced energy response
AU - Jaehyeok Lee
AU - Iuegyun Hong
AU - Jinhong Park
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2608.28146
UR - https://arxiv.org/abs/2608.28146
AB - Relativistic effective field theory predicts a topological energy response to a gravitational field that appears at third order in spatial gradients. Here, we investigate how this response emerges in the nonrelativistic Haldane model using a microscopic lattice formulation of curvature-induced deformations. We find that the leading first-order energy response is nonuniversal and depends on the bond-resolved structure of the deformation; in particular, it vanishes for a symmetric modulation of the three nearest-neighbor hoppings. At third order, the curvature-induced energy response contains a bond-symmetric component together with nonuniversal bond-dependent contributions. The bond-symmetric component, which is isolated by a uniform modulation of the three hoppings, exhibits a universal discontinuity across the topological transition whose magnitude agrees with the relativistic gravitational Chern--Simons prediction. Thus, although the full curvature-induced energy response generally contains nonuniversal lattice contributions, its third-order response retains a universal topological component beyond the relativistic limit.
ER -