Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians
cond-mat.str-el, hep-th, quant-ph
Submitted: 2026-05-29
Updated: 2026-09-18
Comments: 7+16 pages, 3+7 figures. Typos fixed, references added. New results included: extraction of the central charge for a family of iMPS and scaling dimensions for several critical chains
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
Terminology
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.
Sources
- Nonequilibrium Probes of Quantum Geometry in Gapless Systems
- Observing conformal Floquet dynamics on a digital quantum processor
- Operator content of real-space entanglement spectra at conformal critical points
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