Related papers: Instantaneous response and quantum geometry of ins…
Quantum geometric tensor (QGT), which is usually obtained by evaluating the quantum distance between Bloch states parametrized by momentum, plays a key role in exploring the exotic responses of quantum materials. Herein, we revisit the…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
The aim of this memoir for "Habilitation \`a Diriger des Recherches" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by…
We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference…
In band insulators, where the Fermi surface is absent, adiabatic transport is allowed only due to the geometry of the Hilbert space. By driving the system at a small but finite frequency $\omega$, transport is still expected to depend…
The quantum geometric tensor (QGT), whose real and imaginary parts define the quantum metric and Berry curvature, encodes the intrinsic geometry of quantum states. While electronic QGT has been directly observed and linked to various…
We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We…
Generative modeling is one of the most promising applications of quantum machine learning, yet training and deploying Quantum Generative Models (QGMs) on near-term hardware remains effectively intractable due to prohibitive gradient…
Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…
We propose the theory of quantum gravity with interactions introduced by topological principle. The fundamental property of such a theory is that its energy-momentum tensor is an BRST anticommutator. Physical states are elements of BRST…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG):The quantum kinematics of AQG is determined by an abstract $*-$algebra generated by a countable set of elementary operators labelled…
The quantum geometric tensor (QGT) characterizes the local geometry of quantum states, and its components directly account for the dynamical effects observed, e.g., in condensed matter systems. In this work, we address the problem of…
We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum…
We investigate the post-quench dynamics of the quantum geometric tensor (QGT) of 1D periodic systems with a suddenly changed Hamiltonian. The diagonal component with respect to the crystal momentum gives a metric corresponding to the…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
We introduce the concept of "quantum geometric nesting'' (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence…
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a…