aiqbench analysis
This research presents a novel wave-function-based method to extract the central charge in conformal field theories by analyzing ground-state overlaps under spatial $q$-Möbius deformations. By applying this lattice estimator to critical quantum chains and topological edge modes, the study offers a robust probe for universal geometric structures in entanglement spectra without relying on traditional anomaly calculations. Such techniques advance the toolkit for characterizing critical systems and topological phases using purely microscopic quantum data.
Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians
arXiv:2606.00214v2 Announce Type: replace-cross 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 $q$-M\"obius 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.
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.
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
Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2606.00214 [cond-mat.str-el]
(or arXiv:2606.00214v2 [cond-mat.str-el] for this version)
Full text under the publisher's open licence · 190 words
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