Related papers: Semiclassical quantization conditions in strained …
Topological flat bands have gained extensive interest as a platform for exploring the interplay between nontrivial band topology and correlation effects. In recent studies, strongly correlated phenomena originating from a topological flat…
Moir\'e lattices have served as the ideal quantum simulation platform for exploring novel physics due to the flat electronic bands resulting from the long wavelength moir\'e potentials. However, the large sizes of this type of system…
Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T$_c$ materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter,…
We present a method for computing first order asymptotics of semiclassical spectra for 1-D Bogoliubov-de Gennes (BdG) Hamiltonian from Supraconductivity, which models the electron/hole scattering through two SNS junctions. This involves: 1)…
We derive the boundary conditions for MoS$_2$ and similar transition-metal dichalcogenide honeycomb (2H polytype) monolayers with the same type of $\mathbf{k}\!\cdot\!\mathbf{p}$ Hamiltonian within the continuum model around the K points.…
Let $\hat H$ be an h-admissible pseudodifferential operator whose principal symbol, $H$, has a unique non-degenerate global minimum. We give a simple proof that the semi-classical asymptotics of the eigenvalues of $\hat H$ corresponding to…
We study by the Gutzwiller approximation the melting of the valence bond crystal phase of a bilayer Hubbard model at sufficiently large inter-layer hopping. We find that a superconducting domain, with order parameter $d_{z^2-r^2}$, $z$…
We show that, when $N$ is a multiple of 6 ($N=6m$, $m$ integer), the \SU{N} Heisenberg model on the honeycomb lattice with $m$ particles per site has a clear tendency toward chiral order as soon as $m\geq 2$. This conclusion has been…
The goal of this paper is to find the quantization conditions of Bohr-Sommerfeld of k quantum Hamiltonians acting on the euclidian space of dimension n, depending on a small parameter h, and which commute to each other. That is we…
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…
We give Bohr-Sommerfeld quantization rules corresponding to quasi-eigenvalues for a 1-D h-Pseudodifferential operator with real principal symbol and verifying PT symmetry.
The existence of Bloch flat bands provides an facile pathway to realize strongly correlated phenomena in materials. Using density-functional theory and tight-binding approach, we show that the flat bands can form in twisted bilayer of…
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical…
We study the localization properties of generalized, two- and three-dimensional Lieb lattices, $\mathcal{L}_2(n)$ and $\mathcal{L}_3(n)$, $n= 1, 2, 3$ and $4$, at energies corresponding to flat and dispersive bands using the transfer matrix…
Coquelin et al. studied biperiodic semiconductor superlattices, which consist of alternating cell types, one with wide wells and the other narrow wells, separated by equal strength barriers. If the wells were identical, it would be a simply…
We investigate the spectral properties of a quasi-one-dimensional lattice in two possible dimerisation configurations. Both configurations are characterized by the same lattice topology and the identical spectra containing a flat band at…
We apply recently developed smooth boundary conditions to the quantum Monte Carlo simulation of the two-dimensional Hubbard model. At half-filling, where there is no sign problem, we show that the thermodynamic limit is reached more rapidly…
Rhombohedral graphene (rG) aligned with hexagonal boron nitride (hBN) has been shown to host flat bands that stabilize various strongly correlated quantum phases, including Mott insulators, integer, and fractional quantum anomalous Hall…
We consider the Bochner Laplacian on high tensor powers of a positive line bundle on a closed symplectic manifold (or, equivalently, the semiclassical magnetic Schr\"odinger operator with the non-degenerate magnetic field). We assume that…
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…