Bruno Mera
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Density Matrix Geometry and Sum Rules Open
Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM…
Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity Open
We present a new geometric characterization of generalized Landau levels (GLLs). The GLLs are a generalization of Landau levels to non-uniform Berry curvature, and are mathematically defined in terms of a holomorphic curve -- an ideal Kähl…
Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice Open
Realizing topological flat bands with tailored single-particle Hilbert spaces is a critical step toward exploring many-body phases, such as those featuring anyonic excitations. One prominent example is the Kapit-Mueller model, a variant of…
Uniqueness of Landau levels and their analogs with higher Chern numbers Open
Landau levels are the eigenstates of a charged particle in two dimensions under a magnetic field and are at the heart of the integer and fractional quantum Hall effects, which are two prototypical phenomena showing topological features. Fo…
Theory of Generalized Landau Levels and Implication for non-Abelian States Open
Quantum geometry is a fundamental concept to characterize the local properties of quantum states. It is recently demonstrated that saturating certain quantum geometric bounds allows a topological Chern band to share many essential features…
Experimental demonstration of topological bounds in quantum metrology Open
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of ba…
Uniqueness of Landau levels and their analogs with higher Chern numbers Open
Landau levels are the eigenstates of a charged particle in two dimensions under a magnetic field, and are at the heart of the integer and fractional quantum Hall effects, which are two prototypical phenomena showing topological features. F…
Nontrivial quantum geometry of degenerate flat bands Open
The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and no…
Singular connection approach to topological phases and resonant optical responses Open
We introduce a class of singular connections as an alternative to the Berry connection for any family of quantum states defined over a parameter space. We find a natural application of the singular connection in the context of transition d…
Information geometry of quantum critical submanifolds: Relevant, marginal, and irrelevant operators Open
We analyze the thermodynamical limit of the quantum metric along critical submanifolds of theory space. Building upon various results previously known in the literature, we relate its singular behavior to normal directions, which are natur…
Experimental demonstration of topological bounds in quantum metrology Open
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of ba…
Nontrivial quantum geometry of degenerate flat bands Open
The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and no…
Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers Open
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play comp…
Report on scipost_202111_00053v1 Open
This lecture note adresses the correspondence between spectral flows, often associated to unidirectional modes, and Chern numbers associated to degeneracy points.The notions of topological indices (Chern numbers, analytical indices) are in…
Engineering geometrically flat Chern bands with Fubini-Study Kähler structure Open
We describe a systematic method to construct models of Chern insulators whose Berry curvature and the quantum volume form coincide and are flat over the Brillouin zone; such models are known to be suitable for hosting fractional Chern insu…
Report on 2106.00800v3 Open
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics.In this context, two fundamental geometric quantities play complementary role…
Report on 2106.00800v3 Open
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics.In this context, two fundamental geometric quantities play complementary role…
Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics Open
We study the change of the Laughlin states under large deformations of the geometry of the sphere and the plane, associated with Mabuchi geodesics on the space of metrics with Hamiltonian $S^1$-symmetry. For geodesics associated with the s…
Relations between topology and the quantum metric for Chern insulators Open
We investigate relations between topology and the quantum metric of two-dimensional Chern insulators. The quantum metric is the Riemannian metric defined on a parameter space induced from quantum states. Similar to the Berry curvature, the…
Kähler geometry and Chern insulators: Relations between topology and the quantum metric Open
We study Chern insulators from the point of view of K\\"ahler geometry, i.e.\nthe geometry of smooth manifolds equipped with a compatible triple consisting\nof a symplectic form, an integrable almost complex structure and a Riemannian\nmet…
Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions Open
We provide a natural generalization of a Riemannian structure, i.e., a\nmetric, recently introduced by Sj\\"{o}qvist for the space of non degenerate\ndensity matrices, to the degenerate case, i.e., the case in which the\neigenspaces have d…
The product of two independent Su-Schrieffer-Heeger chains yields a two-dimensional Chern insulator Open
We provide an extensive look at Bott periodicity in the context of complex\ngapped topological phases of free fermions. In doing so, we remark on the\nexistence of a product structure in the set of inequivalent phases induced by\nthe exter…
The external tensor product of topological phases of free fermions: "SSH times SSH equals Chern insulator'' Open
We provide an extensive look at Bott periodicity in the context of complex gapped topological phases of free fermions. In doing so, we remark on the existence of a product structure in the set of inequivalent phases induced by the external…
On the minmax regret for statistical manifolds: the role of curvature Open
Model complexity plays an essential role in its selection, namely, by choosing a model that fits the data and is also succinct. Two-part codes and the minimum description length have been successful in delivering procedures to single out t…
Localization anisotropy and complex geometry in two-dimensional insulators Open
The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic …
Topologically Protected Quantization of Work Open
The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this a…
Information Geometry in the Analysis of Phase Transitions Open
The Uhlmann connection is a mixed state generalization of the Berry connection.The latter has a very important role in the study of topological phases at zero temperature.Closely related, the fidelity is an information theoretical measure …
Topological phase transitions in 1D and 2D topological superconductors with long-range effects Open
The Uhlmann connection is a mixed state generalisation of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretica…