Related papers: "Quantum Geometric Nesting" and Solvable Model Fla…
We investigate aspects of the relation between the quantum geometry of the normal state (NS) and the superconducting phase, through the lens of non-locality. By relating band theory to quantum estimation theory, we derive a direct…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct new exactly solvable n…
We review the theoretical description of the role of quantum geometry in superfluidity and superconductivity of multiband systems, with focus on flat bands where quantum geometry is wholly responsible for supercurrents. This review differs…
We explore electronic and structural properties of Fm$\overline{3}$m Lu-H-N structures with specific N,H ordering as plausible candidates for near-ambient superconductivity possibly originating from their remarkably narrow hydrogen-based…
Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in…
We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the…
Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry…
A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed. The infinite hierarchy of quantum conservation laws and…
We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using…
Systems hosting flat bands offer a powerful platform for exploring strong correlation physics. Theoretically topological degeneracy rising in systems with non-trivial topological orders on periodic manifolds of non-zero genus can generate…
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…
We propose ferromagnetism that occurs in electrons at a saddle point with band touching, which we call the singular saddle point. At the singular saddle point, the divergent quantum metric induces ferromagnetic correlation, and the…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
In flat-band systems with quenched kinetic energy, most of the conventional length scales related to the band dispersion become ineffectual. Although a few geometric length scales, such as the quantum metric length, can still be defined,…
Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting many-body systems. Their essential merit lies…
We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many body states in which an arbitrary…
With the advent of gravitational wave detectors employing squeezed light, quantum waveform estimation---estimating a time-dependent signal by means of a quantum-mechanical probe---is of increasing importance. As is well known, backaction of…
With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an…
We present the appearance of nearly flat band states with nonzero Chern numbers in a two-dimensional "diamond-octagon" lattice model comprising two kinds of elementary plaquette geometries, diamond and octagon, respectively. We show that…