Related papers: "Quantum Geometric Nesting" and Solvable Model Fla…
The absence of a well-defined Fermi surface in flat-band systems challenges the conventional understanding of instabilities toward Landau order based on nesting. We investigate the existence of an intrinsic nesting structure encoded in the…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We construct a Hubbard model with a nearly flat band whose quantum geometry can be tuned independently of the energy dispersion and the Coulomb interaction. We show that, when the nearly flat band is half-filled, the exact ground state of…
The interplay of quantum geometry and interactions determines the correlated state properties of flat bands. Here, we investigate the ideal quantum geometry (IQG), i.e., the property that the trace of quantum metric equals the Berry…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
Despite its abundance in nature, predicting the occurrence of ferromagnetism in the ground state is possible only under very limited conditions such as in a flat band system with repulsive interaction or in a band with a single hole under…
Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive…
A fully-connected qubit network is considered, where every qubit interacts with every other one. When the interactions between the qubits are homogeneous, the system is a special case of the finite Lipkin-Meshkov-Glick model. We propose a…
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field…
We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
A singular flat band(SFB), a distinct class of the flat band, has been shown to exhibit various intriguing material properties characterized by a geometric quantity of the Bloch wave function called the quantum distance. We present a…
The quantum state transmission (QST) through the medium of high-dimensional many-particle system is studied with a symmetry analysis. We discover that, if the spectrum matches the symmetry of a fermion or boson system in a certain fashion,…
The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the…
The quasinormal modes (QNM's) of gravitational systems modeled by the Klein-Gordon equation with effective potentials are studied in analogy to the QNM's of optical cavities. Conditions are given for the QNM's to form a complete set, i.e.,…
Let group generators having finite-dimensional representation be realized as Hermitian linear differential operators without nhomogeneous terms as takes place, for example, for the SO(n) group. Then orresponding group Hamiltonians…
Quantum Generative Adversarial Networks (QGANs) have emerged as a promising direction in quantum machine learning, combining the strengths of quantum computing and adversarial training to enable efficient and expressive generative modeling.…