Ground State Of Model Research Articles

Constructing Hubbard models for the hydrogen chain using sliced-basis density matrix renormalization group

Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and to construct low-energy effective Hubbard-like models. The downfolding procedure first involves a change of basis to a set of atom-centered Wannier functions constructed from the natural orbitals of the exact DMRG one-particle density matrix. The Wannier function model is then reduced to a fewer-parameter Hubbard-like model, whose parameters are determined by minimizing the expectation value of the Wannier Hamiltonian in the ground state of the Hubbard Hamiltonian. This indirect variational procedure not only yields compact and simple models for the hydrogen chain, but also allows us to explore the importance of constraints in the effective Hamiltonian, such as the restricting the range of the single-particle hopping and two-particle interactions, and to assess the reliability of more conventional downfolding. The entanglement entropy for a model's ground state, cut in the middle, is an important property determining the ability of DMRG and tensor networks to simulate the model, and we study its variation with the range of the interactions. Counterintuitively, we find that shorter ranged interactions often have larger entanglement.

Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics

In the study of strongly-correlated, many-electron systems, the Hubbard Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multi-band in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenate, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high accuracy modeling of the HK model's ground state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than 1% can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. The results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly-correlated materials using AFQMC.

Rigorous Results Concerning the Holstein–Hubbard Model

The Holstein model has been widely accepted as a model comprising electrons interacting with phonons; analysis of this model's ground states was accomplished two decades ago. However, the results were obtained without completely taking repulsive Coulomb interactions into account. Recent progress has made it possible to treat such interactions rigorously; in this paper, we study the Holstein--Hubbard model with repulsive Coulomb interactions. The ground state properties of the model are investigated; in particular, the ground state of the Hamiltonian is proven to be unique for an even number of electrons on a bipartite connected lattice. In addition, we provide a rigorous upper bound on charge susceptibility.

Exactly solvable model of topological insulator realized on spin- $\tfrac{1}{2}$ lattice

In this paper we propose an exactly solvable model of a topological insulator defined on a spin-1/2 square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin-1/2 Kitaev sublattice. The presented model, whose ground state is a non-trivial topological phase, is solved exactly. We have found out that various phase transitions without gap closing at the topological phase transition point outline the separate states with different topological numbers. We provide a detailed analysis of the model's ground-state phase diagram and demonstrate how quantum phase transitions between topological states arise. We have found that the states with both the same and different topological numbers are all separated by the quantum phase transition without gap closing. The transition between topological phases is accompanied by a rearrangement of the spin subsystem's spectrum from band to flat-band states.

Ground state and excitations of a four-component fermion model

The properties of the ground state and excitations of a four-component Hubbard-like model are studied by the Lieb-Schultz-Mattis approach. It is proven rigorously that the ground state of the model is nondegenerate and excitations are gapless at all band fillings.

Chemical and photophysical properties of AuI, AuII, AuIII, and AuI-dimer complexes

Abstract Various AuI, AuII, AuIII, and AuI-dimer complexes were probed using density-functional theory (DFT), specifically the B3PW91 hybrid functional, and relativistic effective core potentials. The research aimed to investigate the photophysical properties of gold complexes, and inspect the factors that influence the geometry and bonding properties of gold compounds. The results illustrate that the geometry of AuI complexes (ground-state singlet) is very sensitive to the electronic nature of the ligands: σ-donors give a two-coordinate, linear shape; however, π-acceptors yield a three-coordinate, trigonal planar geometry. Doublet AuIIL3 complexes distort to a T-shape coordination geometry, and are thus ground state models of the corresponding AuIL3 triplet excitons. The disproportionation of AuIIL3 to AuIL3 and AuIIIL3 complexes is endothermic for all ligands investigated, suggesting that these complexes, neglected by experimentalists, are interesting subjects for study and may display unique photochemical properties. For dimeric AuI complexes, the optimized triplet exciton shows a Jahn–Teller distortion around only one of the gold centers. Furthermore, the Au–Au distance is reduced in the dimer excited state versus the ground state, which should yield interesting Stokes’ shifts.

Ground State of the Classical XY Model with Twofold Symmetry Breaking Field Pertaining to the Devil's Staircase

The Ising model and the classical XY model with frustrating second nearest neighbour interaction in an axial direction have qualitatively different properties to each other both at ground state and in the finite temperature. The XY model exposed to the symmetry breaking field with twofold symmetry is here introduced, which is reduced to the Ising model, that is, the ANNNI model in the limit of the strong field strength. The ground state of this model is examined, in which the freedom of the XY spin is shown to be suppressed at rather small strength of the symmetry breaking field and accordingly the Ising properties dominate in large area on an interaction parameter versus field diagram, while the freedom of XY spin survives only at an area with weak field. This result seems to explain why the successive phase transitions observed in ferro- and antiferro-electric smectic liquid crystals can occur.

Improved finite-lattice method for estimating the zero-temperature properties of two-dimensional lattice models

The well-known finite-lattice method for the calculation of the properties of quantum spin systems on a two-dimensional lattice at zero temperature was introduced in 1978. The method has now been greatly improved for the square lattice by including finite lattices based on parallelogram tiles as well as the familiar finite lattices based on square tiles. Dozens of these new finite lattices have been tested and graded using the [Formula: see text] ferromagnet. In the process new and improved estimates have been obtained for the XY model's ground-state energy per spin, ε0 = −0.549 36(30) and spontaneous magnetization per spin, m = 0.4349(10). Other properties such as near-neighbour, zero-temperature spin–spin correlations, which appear not to have been calculated previously, have been estimated to high precision. Applications of the improved finite-lattice method to other models can readily be carried out.

Multiatom interactions in the fcc Ising binary alloy: Low-temperature behavior and Monte Carlo simulations.

We investigate an Ising model of an ordering binary alloy on the face-centered-cubic lattice, such as Cu-Au. This model contains multiatom interactions on the triangles and tetrahedra of the lattice as well as the usual repulsions on the nearest-neighbor bonds. We examine the model's ground states and its low-temperature equilibrium states: There are an infinite number of the former but only a few of the latter. We also study its phase diagram using Monte Carlo simulations, which confirm the broad conclusions of previous cluster-variation-method calculations, particularly near stoichiometry. Even small triangular interactions can introduce dramatic asymmetry into the phase diagram, making it similar to those observed in real alloys.