Publications (29)
Nontrivial quantum geometry of degenerate flat bands
Bruno Mera, Johannes Mitscherling
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 Che…
The Uhlmann connection in fermionic systems undergoing phase transitions
Bruno Mera, Chrysoula Vlachou, Nikola PaunkoviÄ +1
We study the behaviour of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyse some of the paradigmatic cases of topological insula…
Localization anisotropy and complex geometry in two-dimensional insulators
Bruno Mera
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…
Hall viscosity from metric-sensitive dichroic probes
Alberto Nardin, Bruno Mera, Anaïs Defossez +3
Hall viscosity characterizes the geometric response of a quantum Hall droplet to deformations of the underlying metric, yet it has remained difficult to measure directly. We propos…
Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
Bruno Mera, Tomoki Ozawa
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…
Theory of Generalized Landau Levels and Implication for non-Abelian States
Zhao Liu, Bruno Mera, Manato Fujimoto +2
Quantum geometry is a fundamental concept to characterize the local properties of quantum states. It is recently demonstrated that saturating certain quantum geometric bounds allow…
Kähler geometry and Chern insulators: Relations between topology and the quantum metric
Bruno Mera, Tomoki Ozawa
We study Chern insulators from the point of view of Kähler geometry, i.e. the geometry of smooth manifolds equipped with a compatible triple consisting of a symplectic form, an in…
On the minmax regret for statistical manifolds: the role of curvature
Bruno Mera, Paulo Mateus, Alexandra M. Carvalho
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 ha…
Experimental demonstration of topological bounds in quantum metrology
Min Yu, Xiangbei Li, Yaoming Chu +6
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…
Information geometric analysis of long range topological superconductors
Syed Tahir Amin, Bruno Mera, Nikola PaunkoviÄ +1
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…
Perfect elliptic dichroism: Probing the metric of anisotropic quantum Hall droplets
Bruno Mera, Alberto Nardin, Anaïs Defossez +3
Understanding the geometry of quantum Hall systems is a central challenge in modern condensed matter physics. We introduce a framework for probing the geometric structure of quantu…
Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
Hector Silva, Bruno Mera, Nikola PaunkoviÄ
We provide a natural generalization of a Riemannian structure, i.e., a metric, recently introduced by Sjöqvist for the space of non degenerate density matrices, to the degenerate…
Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
Bruno Mera, Chrysoula Vlachou, Nikola PaunkoviÄ +2
We study finite-temperature Dynamical Quantum Phase Transitions (DQPTs) by means of the fidelity and the interferometric Loschmidt Echo (LE) induced metrics. We analyse the associa…
Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity
Carolina Paiva, Jie Wang, Tomoki Ozawa +1
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 mathematical…
Density Matrix Geometry and Sum Rules
Guangyue Ji, David E. Palomino, Nathan Goldman +4
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…
A theorem regarding families of topologically non-trivial fermionic systems
Bruno Mera, Miguel A. N. Araújo, VÃtor R. Vieira
We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a topologica…
Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics
Gabriel Matos, Bruno Mera, José M. Mourão +2
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 Hami…
The product of two independent Su-Schrieffer-Heeger chains yields a two-dimensional Chern insulator
Bruno Mera
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 structur…
Topologically protected quantization of work
Bruno Mera, Krzysztof Sacha, Yasser Omar
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…
Singular connection approach to topological phases and resonant optical responses
Bruno Mera, Tomoki Ozawa
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 applicatio…
Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
Xin Shen, Guangyue Ji, Jinjie Zhang +4
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…
Relations between topology and the quantum metric for Chern insulators
Tomoki Ozawa, Bruno Mera
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 induc…
Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators
Bruno Mera, Nikola PaunkoviÄ, Syed Tahir Amin +1
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…
Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
Bruno Mera, Chrysoula Vlachou, Nikola PaunkoviÄ +1
We perform the fidelity analysis for Boltzmann-Gibbs-like states in order to investigate whether the topological order of 1D fermionic systems at zero temperature is maintained at…
Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space
Yoshinori Hashimoto, Bruno Mera, Tomoki Ozawa
We prove the rigidity of isotropic harmonic maps from a 2-torus to a complex projective space, when they are constructed from holomorphic embeddings associated to complete linear s…
Uniqueness of Landau levels and their analogs with higher Chern numbers
Bruno Mera, Tomoki Ozawa
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…
Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
Bruno Mera, Tomoki Ozawa
We propose a microscopic, weak-coupling mechanism by which generic Chern bands asymptotically relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leg…
Quantum Hall States response to toroidal geometry deformation
Bruno Mera, José M. Mourão, João P. Nunes +1
In this paper, we apply techniques of geometric quantization to study the response of the integer and fractional quantum Hall effects to toroidal geometry deformation. The main met…
Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
Bruno Mera, Anwei Zhang, Nathan Goldman
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,…