Related papers: The bilinear-biquadratic model on the complete gra…
The low-energy properties of the two-dimensional Heisenberg model with spin-$\frac{1}{2}$ on a square lattice are investigated on the basis of the local dimer order. The lattice is divided into square blocks consisting of the quartet of…
A simple derivation of the effective spin-wave Hamiltonian for a double-exchange system with infinitely large Hund's-rule coupling is demonstrated. The formalism can be applied to models with arbitrary range of hopping as well as those with…
Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model…
We first study a free particle on an $(n-1)$-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schr\"odinger representation and a Hamilton-Jacobi…
We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge…
A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…
A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically…
The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect…
An interacting-boson-model-1 (IBM-1) Hamiltonian, derived from self-consistent mean-field calculations using a Skyrme energy density functional is employed for the study of energy spectra and $B(E2)$ transition strengths in the even-even…
We investigate entanglement spectra of the SO(3) bilinear-biquadratic spin-1 chain, a model with phases exhibiting spontaneous symmetry breaking (both translation and spin rotation), points of enlarged symmetry, and a symmetry-protected…
Effect of quantum fluctuations concerned with the orbital degrees of freedom is discussed for the model with SU(4) symmetry in one dimension. An effective Hamiltonian is derived from the orbitally degenerate Hubbard model at quarter…
We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the Quantum Field Theory (QFT)…
As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…
We consider a network of n spin 1/2 systems which are pairwise interacting via Ising interaction and are controlled by the same electro-magnetic control field. Such a system presents symmetries since the Hamiltonian is unchanged if we…
We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level…
We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related…
In this article, we consider fixed spin 1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give some asymptotic expansions for the ground state and the ground state energy of the…
We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin $S$, which in the case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising model. For…
Energy versus magnetic-field diagram of the spin-$1$ Haldane system with an impurity bond is studied in terms of spin-1/2 degree of freedom at the sites neighboring the impurity bond by means of analytical method. We examine the equivalence…
We study the Tavis-Cummings model with three modes of oscillation by using four different algebraic methods: the Bogoliubov transformation, the normal-mode operators, and the tilting transformation of the $SU(1,1)$ and $SU(2)$ groups. The…