Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExact ground states of correlated electrons on pentagon chains
118
0
0.0
(
0
)
Authors
Zsolt Gulacsi
Ask ChatGPT about the research
No Arabic abstract
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 composite operators as a linear combination of creation operators acting on the sites of finite blocks. In the same step, the interaction is also transformed to obtain terms which require for their minimum eigenvalue zero at least one electron on each site. The transformed Hamiltonian matches the original Hamiltonian through a nonlinear system of equations whose solutions place the deduced ground states in restricted regions of the parameter space. In the second step, nonlocal product wave functions in position space are constructed. They are proven to be unique ground states which describe non-saturated ferromagnetic and correlated half metallic states. These solutions emerge when the strength of the Hubbard interaction $U_i$ is site dependent inside the unit cell. In the deduced phases, the interactions tune the bare dispersive band structure such to develop an effective upper flat band. We show that this band flattening effect emerges for a broader class of chains and is not restricted to pentagon chains. For the characterization of the deduced solutions, uniqueness proofs, exact ground state expectation values for long-range hopping amplitudes and correlation functions are also calculated. The study of physical reasons which lead to the appearance of ferromagnetism has revealed a new mechanism for the emergence of an ordered phase, described here in details (because of lack of space see the continuation in the paper).
rate research
Read More
We model conducting pentagon chains with a multi orbital Hubbard model and prove that well below half filling exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimesion and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat band ferromagnetism requires, where on every site a Hubbard term is present. In our case only a small percentage of, even randomly distributed, sites are only interacting.
We derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4)$times$U(4) symmetry, and we find that the exact ground states at integer filling $-4le ule 4$ relative to charge neutrality are Chern insulators of Chern numbers $ u_C=4-| u|,2-| u|,cdots,| u|-4$, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $ u=0,pm2$ has exact ground states of Chern number $0$, while $ u=pm1,pm3$ has perturbative ground states of Chern number $ u_C=pm1$, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $ u_C=0$ ($0<| u_C|<4-| u|$) at integer fillings $ u$ are fully (partially) intervalley coherent, while the insulator states with Chern number $| u_C|=4-| u|$ are valley polarized. However, for $0<| u_C|le4-| u|$, the fully intervalley coherent states are highly competitive (0.005meV/electron higher). At nonzero magnetic field $|B|>0$, a first-order phase transition for $ u=pm1,pm2$ from Chern number $ u_C=text{sgn}( u B)(2-| u|)$ to $ u_C=text{sgn}( u B)(4-| u|)$ is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.
The competition between kinetic energy and Coulomb interactions in electronic systems can lead to complex many-body ground states with competing superconducting, charge density wave, and magnetic orders. Here we study the low temperature phases of a strongly interacting zinc-oxide-based high mobility two dimensional electron system that displays a tunable metal-insulator transition. Through a comprehensive analysis of the dependence of electronic transport on temperature, carrier density, in-plane and perpendicular magnetic fields, and voltage bias, we provide evidence for the existence of competing correlated metallic and insulating states with varying degrees of spin polarization. Our system features an unprecedented level of agreement with the state-of-the-art Quantum Monte Carlo phase diagram of the ideal jellium model, including a Wigner crystallization transition at a value of the interaction parameter $r_ssim 30$ and the absence of a pure Stoner transition. In-plane field dependence of transport reveals a new low temperature state with partial spin polarization separating the spin unpolarized metal and the Wigner crystal, which we examine against possible theoretical scenarios such as an anti-ferromagnetic crystal, Coulomb induced micro-emulsions, and disorder driven puddle formation.
We use the matrix product approach to construct all optimum ground states of general anisotropic spin-2 chains with nearest neighbour interactions and common symmetries. These states are exact ground states of the model and their properties depend on up to three parameters. We find three different antiferromagnetic Haldane phases, one weak antiferromagnetic and one weak ferromagnetic phase. The antiferromagnetic phases can be described as spin liquids with exponentially decaying correlation functions. The variety of phases found with the matrix product ansatz also gives insight into the behaviour of spin chains with arbitrary higher spins.
Low-dimensional electron systems fabricated from quantum matter have in recent years become available and are being explored with great intensity. This article gives an overview of the fundamental properties of such systems and summarizes the state of the field. We furthermore present and consider the concept of artificial atoms fabricated from quantum materials, anticipating remarkable scientific advances and possibly important applications of this new field of research. The surprising properties of these artificial atoms and of molecules or even of solids assembled from them are presented and discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
