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The multi-state geometry of shift current and polarization

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arxiv 2409.16358 v2 pith:4UY42WYC submitted 2024-09-24 cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-sciquant-ph

classification cond-mat.str-elcond-mat.mes-hallcond-mat.mtrl-sciquant-ph
keywords geometrymulti-statepolarizationpropertiesquantumstatesapplicationsapproach
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The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state geometry is necessary to explain properties involving Bloch states of multiple bands, such as optical transitions. To this end, we employ quantum state projectors to develop an explicitly gauge-invariant formalism and demonstrate its power with applications to non-linear optics and the theory of electronic polarization. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization, clarifies the treatment of band degeneracies, and reveals its decomposition into the sum of the skewness of the occupied states and intrinsically multi-state geometry. The projector approach is applied to calculate non-linear optical properties of transition metal dichalcogenides (TMDs) layers, using previously calculated minimal tight-binding models, and demonstrated analytically on a three-band generalization of the Rice-Mele chain to elucidate the different contributions. We close with comments on further applications of the projector operator approach to multi-state geometry.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Multi-State Geometry of Density Matrices and Rectification Sum Rules

    cond-mat.mes-hall 2026-08 accept novelty 7.0 of 10

    Rectification current in insulators obeys a zero-temperature sum rule expressed as a ground-state cumulant minus a many-body multi-state geometric tensor, generalizing known single-particle results.

  2. Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective

    cond-mat.mes-hall 2025-07 accept novelty 7.0 of 10

    The Bures distance between an initial and a time-evolved density matrix defines a time-dependent quantum metric and connection, extending many-body quantum geometry beyond the quantum metric to higher-order correlatio...

  3. Imaginary Time Formalism for Causal Nonlinear Response Functions

    cond-mat.mes-hall 2025-06 conditional novelty 6.0 of 10

    Causal n-th order response functions are obtained, at every order, by analytic continuation of the corresponding imaginary-time Matsubara functions.

  4. Probing quantum geometry with two-dimensional nonlinear optical spectroscopy

    cond-mat.mes-hall 2025-06 conditional novelty 6.0 of 10

    Two-dimensional coherent spectroscopy can isolate and measure the imaginary part of the multi-band quantum connection through the diagonal second-order conductivity under time-reversal symmetry.

  5. Quantum Geometry Phenomena in Condensed Matter Systems

    cond-mat.str-el 2025-08 conditional novelty 2.0 of 10

    Quantum geometry, especially the quantum metric, is surveyed as a unifying framework for a wide range of transport and optical phenomena, with experimental confirmation in several materials.

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