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Ge atoms segregating on zirconium diboride thin films grown on Ge(111) were found to crystallize into a two-dimensional bitriangular structure which was recently predicted to be a flat band material. Angle-resolved photoemission experiments…
The energy dispersion of fermions or bosons vanishes in momentum space if destructive quantum interference occurs in a frustrated Kagome lattice with only nearest-neighbour (NN) hopping. A discrete flat band (FB) without any dispersion is…
Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in…
Quantum Chromodynamics and Quantum Electrodynamics, both renormalizable quantum field theories with a small number of precisely constrained input parameters, dominate the dynamics of the quarks and gluons - the underlying building blocks of…
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a…
We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann…
Flat-band topologies and localizations in non-interacting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in…
The origin of many quantum-material phenomena is intimately related to the presence of flat electronic bands. In quantum simulation, such bands have been realized through line-graph lattices, a class of lattices known to exhibit flat bands.…
We study the spectral properties of a system of electrons interacting through long-range Coulomb potential on a one-dimensional chain. When the interactions dominate over the electronic bandwidth, the charges arrange in an ordered…
In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build quantum simulators, which would open up the…
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…
Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and…
In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the…
We report on the realization of a multi-orbital system with ultracold atoms in the excited bands of a 3D optical lattice by selectively controlling the band population along a given lattice direction. The lifetime of the atoms in the…
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…
We prove that, contrary to the common belief, the classical Maxwell electrodynamics of a point-like particle may be formulated as an infinite-dimensional Hamiltonian system. We derive well defined quasi-Hamiltonian which possesses direct…
In cavity quantum electrodynamics (QED), light-matter interaction is probed at its most fundamental level, where individual atoms are coupled to single photons stored in three-dimensional cavities. This unique possibility to experimentally…
The pursuit of superconducting-based quantum computers has advanced the fabrication of and experimentation with custom lattices of qubits and resonators. Here, we describe a roadmap to use present experimental capabilities to simulate an…