Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians
Abstract
We show that the conformal anomaly of a (1+1)-dimensional conformal field theory can be extracted directly from a ground-state wave-function overlap associated with a spatial conformal deformation. Focusing on the q-Möbius deformation, we derive an exact overlap formula between the deformed and undeformed ground states, whose exponent directly encodes the central charge. Motivated by this result, we construct a lattice estimator based solely on ground-state overlaps and apply it to representative critical quantum chains and the gapless edge modes of a two-dimensional Chern insulator. Numerical results demonstrate that the resulting overlaps provide a simple and robust probe of the central charge in microscopic models. We further demonstrate that the deformed ground states retain universal geometric structures in their entanglement spectra and entanglement entropies. These results provide a simple wave-function-based route to probing conformal data in critical systems and topological edge modes.
Related
- Projective relativistic dynamics from a quantum Lorentz algebra: time-dependent deformed Hamiltonians on (anti-)de Sitter spaces
- Extracting the Central Sound Speed of Neutron Stars through Intrinsic Stellar Structure Scaling with Reduced Equation-of-State Model Dependence
- Algorithmic overlaps in the Baxter–Wu model: cluster dynamics under Novotny–Evertz updates
- On the gauge invariant boundary condition in open XXZ chains: SoV bases, elementary blocks and overlaps
- A rank-two spherical transform for eigenvector and singular-vector overlaps
BibTeX
@misc{bai2026extracting,
title = {{Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians}},
author = {Chen Bai and Xinyu Sun and Liang-Hong Mo and Hong-Hao Tu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.00214},
eprint = {2606.00214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00214},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians
AU - Chen Bai
AU - Xinyu Sun
AU - Liang-Hong Mo
AU - Hong-Hao Tu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2606.00214
UR - https://arxiv.org/abs/2606.00214
AB - We show that the conformal anomaly of a (1+1)-dimensional conformal field theory can be extracted directly from a ground-state wave-function overlap associated with a spatial conformal deformation. Focusing on the q-Möbius deformation, we derive an exact overlap formula between the deformed and undeformed ground states, whose exponent directly encodes the central charge. Motivated by this result, we construct a lattice estimator based solely on ground-state overlaps and apply it to representative critical quantum chains and the gapless edge modes of a two-dimensional Chern insulator. Numerical results demonstrate that the resulting overlaps provide a simple and robust probe of the central charge in microscopic models. We further demonstrate that the deformed ground states retain universal geometric structures in their entanglement spectra and entanglement entropies. These results provide a simple wave-function-based route to probing conformal data in critical systems and topological edge modes.
ER -