Related papers: Notes on Quantum oscillation for Hatsugai-Kohmoto …
Following nearly a century of research, it remains a puzzle that the low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands. The abundance of interactions in real…
We present a consistent treatment of the quantum Hall effect within the electrostatic approximation. We derive the form of the density of states (DOS) which differs from the usual gaussian shape valid for non-interacting electrons. Below a…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
We analyze the particle-hole symmetric two-dimensional Hubbard model on a square lattice starting from weak-to-moderate couplings by means of the field-theoretical renormalization group (RG) approach up to two-loop order. This method is…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
Recent quantum oscillation experiments on SmB$_6$ pose a paradox, for while the angular dependence of the oscillation frequencies suggest a 3D bulk Fermi surface, SmB$_6$ remains robustly insulating to very high magnetic fields. Moreover, a…
We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact…
Single-orbital Hubbard models exhibit remarkably nontrivial correlation phenomena, even on nonfrustrated bipartite lattices. Some of these, like non-Fermi-liquid metal states, or the coexistence of heavy and light quasi-particles, are…
Interacting quantum many-body systems constitute a fascinating playground for researchers since they form quantum liquids with correlated ground states and low-lying excitations, which exhibit universal behaviour. In fermionic systems, such…
In this paper we study theoretically how the local geometry of the Fermi surface (FS) of a layered conductor can affect quantum oscillations in the thermodynamic observables. We introduce a concrete model of the FS of a layered conductor.…
Effective models focused on pertinent low-energy degrees of freedom have substantially contributed to our qualitative understanding of quantum materials. An iconic example, the Kondo model, was key to demonstrating that the rich phase…
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors…
In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for the…
Quantum simulation is one of the most promising near term applications of quantum computing. Especially, systems with a large Hilbert space are hard to solve for classical computers and thus ideal targets for a simulation with quantum…
We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion…
Quantum oscillation (QO) measurements constitute a powerful method to measure the Fermi surface (FS) properties of metals. The observation of QOs is usually taken as strong evidence for the existence of extremal cross-sectional areas of the…
In cavity quantum materials, entangling strongly correlated electrons with quantum light provides a unique opportunity to explore novel quantum phases and phase transitions absent in conventional solid-state materials. In this study, we…
The Nagaoka ($U=\infty$) limit of the Hubbard model on a square lattice is mapped onto the itinerant-localized Kondo model at infinitely strong coupling. Such a model is well suited to perform quantum Monte Carlo (QMC) simulations to…
Quantum spin liquids represent exotic states of spin systems characterized by long-range entanglement and emergent fractionalized quasiparticles. It is generally believed that disorder is hostile to quantum spin liquids. In our study, we…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…