Related papers: Efficient O(N^1.5) Electronic Structure Computatio…
We show that the electronic structure of the low-energy bands in the small angle-twisted bilayer graphene consists of a series of semi-metallic and topological phases. In particular we are able to prove, using an approximate low-energy…
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…
Twisted multilayer systems, encompassing materials like twisted bilayer graphene (TBG), twisted trilayer graphene, and twisted bilayer transition metal dichalcogenides, have garnered significant attention in condensed matter physics.…
We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with…
Correlated insulators and superconductivity have been observed in "magic-angle" twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these…
We present a symmetry-based calculation of the electronic structure of a compound semiconductor quantum dot (QD) in the sp^3s* tight-binding model including the spin-orbit interaction. The Hamiltonian matrix is diagonalized exactly for CdTe…
We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the…
The ideas of the linear combination of atomic orbitals (LCAO) method, well known from the study of electrons, is extended to the classical wave case. The Mie resonances of the isolated scatterer in the classical wave case, are analogous to…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
Based on a successful description of II-VI ternary alloys, which introduces an empirical bowing parameter to the widely used virtual crystal approximation, we set up a tight-binding Hamiltonian to describe the Zn_{1-y}Cd_ySe_{1-x}Te_x and…
So far the physics of moir\'e graphene bilayers at large, incommensurate rotation angles has been considered uninteresting. It has been held that the interlayer coupling in such structures is weak and the system can be thought of as a pair…
We present some aspects of high precision calculations in the context of Lattice Quantum Field Theory. This work is a collection of three studies done during my Ph.D. period. First we present how to use the reweighting technique to…
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$ gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
We build symmetry adapted maximally localized Wannier states, and construct the low energy tight binding model for the four narrow bands of the twisted bilayer graphene. We do so when the twist angle is commensurate, near the `magic' value,…
The Kohn-Luttinger envelope-function method is generalized to the case of heterostructures with atomically sharp heterojunctions based on lattice-matched layers of related semiconductors with zinc-blende symmetry. For electron states near…
A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (eg. $\theta\sim 1.05^\circ$). In this regime,…
Twisted bilayer graphene with a twist angle of around 1.1{\deg} features a pair of isolated flat electronic bands and forms a strongly correlated electronic platform. Here, we use scanning tunneling microscopy to probe local properties of…
Tailoring electron transfer dynamics across solid-liquid interfaces is fundamental to the interconversion of electrical and chemical energy. Stacking atomically thin layers with a very small azimuthal misorientation to produce moir\'e…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…