Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2408.16057 · Physical review. B./Physical review. B

Corner charge fluctuations and many-body quantum geometry

Xiao-Chuan Wu, Kang-Le Cai, Meng Cheng, Prashant Kumar

Published Mar 10, 2025• 9 citations
arXivHTMLPDF

Abstract

Charge fluctuations in a subregion provide key insights into entanglement and topological properties. We show how many-body quantum geometry manifests in the shape dependence of these fluctuations in 2D insulators, carefully disentangling the universal and nonuniversal aspects. Furthermore, we discuss bounds on many-body quantum geometry and the conditions under which they are saturated, highlighting the roles of spacetime symmetries and wavefunction holomorphicity.

DOI
10.1103/physrevb.111.115124

Related papers

Corner Charge Fluctuations in Higher Dimensions

Xiao-Chuan Wu, Pok Man Tam, Xuyang Liang +4 more

Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect.

arXiv:2605.13971•May 13, 2026•0 citations

Cornering the universal shape of fluctuations

Benoit Estienne, Jean-Marie Stéphan, William Witczak‐Krempa

Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We exemplify our findings with fractional quantum Hall states, topological insulators, scale invariant quantum critical theories, and metals. We suggest experimental tests, and anticipate that our findings can be generalized to other spatial dimensions or geometries. In addition, we highlight the similarities of the fluctuation shape dependence with findings relating to quantum entanglement measures.

arXiv:2102.06223•Nature Communications•Jan 12, 2022•33 citations

Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-Dimensional Insulators

Pok Man Tam, Jonah Herzog-Arbeitman, Jiabin Yu

Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional contribution known to exhibit a universal angle dependence in 2D isotropic and uniform systems. Here we establish that, for generic lattice systems of interacting particles, the corner charge fluctuation is directly related to quantum geometry. We first provide a practical scheme to isolate the corner contribution on lattices and analytically prove that its angle dependence in the "small-angle limit" measures exclusively the integrated quantum metric. A model of a compact obstructed atomic insulator is introduced to illustrate this effect analytically, while numerical verification for various Chern insulator models further demonstrate the experimental relevance of the corner charge fluctuation in a finite-size quantum simulator as a probe of quantum geometry. Last but not least, for free fermions, we unveil an intimate connection between quantum geometry and quantum information through the lens of corner entanglement entropies.

arXiv:2406.17023•Physical Review Letters•Dec 10, 2024•14 citations

Bipartite fluctuations and topology of Dirac and Weyl systems

Loïc Herviou, Karyn Le Hur, Christophe Mora

Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in situations where the relevant particle number is not conserved, leading to additional volume laws scaling with the quantum Fisher information. In the case of the $p+ip$ superconductor, we build a relation between charge fluctuations and the associated winding numbers of Dirac cones in the low-energy sector. Topological aspects of the Hamiltonian in the vicinity of these points induce long-range entanglement in real space. We specifically extract analytical expressions for the corner contributions to bipartite fluctuations. We highlight their differences and similarities with the corner functions of the entanglement entropy which characterize the underlying conformal field theory. We provide a detailed analysis of such fluctuation properties, including the role of gap anisotropy, and discuss higher-dimensional Weyl analogs.

arXiv:1809.08252•Physical review. B./Physical review. B•Feb 19, 2019•13 citations

Many-body higher-order topological invariant for $C_n$-symmetric insulators

Ammar Jahin, Yuan-Ming Lu, Yuxuan Wang

Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa, we propose a well-defined many-body bulk invariant for $C_n$ symmetric higher-order topological insulators, which is valid for both non-interacting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of $C_n$ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as $e/n$ with $C_n$ symmetry, leading to a $\mathbb{Z}_n$ classification for higher-order topological insulators in two dimensions.

arXiv:2401.00050•Dec 29, 2023•0 citations

Many-body higher-order topological invariant for Cn -symmetric insulators

Ammar Jahin, Yuan-Ming Lu, Yuxuan Wang

Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa [arXiv:2302.00800], we propose a well-defined, many-body bulk invariant for ${C}_{n}$-symmetric higher-order topological insulators that is valid for both noninteracting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of ${C}_{n}$ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as $e/n$ with ${C}_{n}$ symmetry, leading to a ${\mathbb{Z}}_{n}$ classification for higher-order topological insulators in two dimensions.

Physical review. B./Physical review. B•May 8, 2024•6 citations
Charge fluctuations in a subregion provide key insights into entanglement and topological properties. We show how many-body quantum geometry manifests in the shape dependence of these fluctuations in 2D insulators, carefully disentangling the universal and nonuniversal aspects. Furthermore, we discuss bounds on many-body quantum geometry and the conditions under which they are saturated, highlighting the roles of spacetime symmetries and wavefunction holomorphicity.
Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect.
Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We exemplify our findings with fractional quantum Hall states, topological insulators, scale invariant quantum critical theories, and metals. We suggest experimental tests, and anticipate that our findings can be generalized to other spatial dimensions or geometries. In addition, we highlight the similarities of the fluctuation shape dependence with findings relating to quantum entanglement measures.
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional contribution known to exhibit a universal angle dependence in 2D isotropic and uniform systems. Here we establish that, for generic lattice systems of interacting particles, the corner charge fluctuation is directly related to quantum geometry. We first provide a practical scheme to isolate the corner contribution on lattices and analytically prove that its angle dependence in the "small-angle limit" measures exclusively the integrated quantum metric. A model of a compact obstructed atomic insulator is introduced to illustrate this effect analytically, while numerical verification for various Chern insulator models further demonstrate the experimental relevance of the corner charge fluctuation in a finite-size quantum simulator as a probe of quantum geometry. Last but not least, for free fermions, we unveil an intimate connection between quantum geometry and quantum information through the lens of corner entanglement entropies.
Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in situations where the relevant particle number is not conserved, leading to additional volume laws scaling with the quantum Fisher information. In the case of the p+ipp+ipp+ip superconductor, we build a relation between charge fluctuations and the associated winding numbers of Dirac cones in the low-energy sector. Topological aspects of the Hamiltonian in the vicinity of these points induce long-range entanglement in real space. We specifically extract analytical expressions for the corner contributions to bipartite fluctuations. We highlight their differences and similarities with the corner functions of the entanglement entropy which characterize the underlying conformal field theory. We provide a detailed analysis of such fluctuation properties, including the role of gap anisotropy, and discuss higher-dimensional Weyl analogs.
Many-body higher-order topological invariant for CnC_nCn​-symmetric insulators
Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa, we propose a well-defined many-body bulk invariant for CnC_nCn​ symmetric higher-order topological insulators, which is valid for both non-interacting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of CnC_nCn​ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as e/ne/ne/n with CnC_nCn​ symmetry, leading to a Zn\mathbb{Z}_nZn​ classification for higher-order topological insulators in two dimensions.
Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa [arXiv:2302.00800], we propose a well-defined, many-body bulk invariant for Cn{C}_{n}Cn​-symmetric higher-order topological insulators that is valid for both noninteracting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of Cn{C}_{n}Cn​ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as e/ne/ne/n with Cn{C}_{n}Cn​ symmetry, leading to a Zn{\mathbb{Z}}_{n}Zn​ classification for higher-order topological insulators in two dimensions.