相关论文: Necessity of orthogonal basis vectors for the two-…
Understanding fundamentals of few-body physics provides an interesting bottom-up approach for the clarification of many-body properties. The remarkable experimental progress in realizing spin-orbit coupling (SOC) in optical Raman lattices…
We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional…
While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the…
Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged.…
The content of this thesis can be broadly summarised into two categories: first, I constructed modified numerical algorithms based on tensor networks to simulate systems of anyons in low dimensions, and second, I used those methods to study…
The Schr\"odinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and…
We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering…
By considering an onsite attraction between a spin-$\uparrow$ and a spin-$\downarrow$ fermion in a multiband tight-binding lattice, here we study the two-body spectrum, and derive an exact relation between the inverse of the effective-mass…
The Schwinger model, which describes lattice quantum electrodynamics in $1+1$ space-time dimensions, provides a valuable framework to investigate fundamental aspects of quantum field theory, and a stepping stone towards non-Abelian gauge…
Objects subjected to a constant force generally increase their velocity over time. This expectation fails whenever their energy is a smooth and periodic function of momentum, resulting in periodic Bloch oscillations instead. Periodic…
The study of nonlinear Schr\"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice) counterparts. They are associated with…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle $\theta\approx\pi$, we observe a…
We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit ($\chi…
We present an ab initio study of the ground state of an ideal coupled two-component gas of ultracold atoms in a one dimensional optical lattice, either bosons or fermions. Due to the internal two-level structure of the atoms, the Brillouin…
Few-magnon bound states in quantum spin chains have been long studied and attracted much recent attentions. For a higher-spin ferromagnetic XXZ chain with single-ion anisotropy, several features regarding the evolution of the low-lying…
We propose a transformation for spin and charge degrees of freedom in one-dimensional lattice systems, constrained to have no doubly occupied sites, that allows direct access to the dynamical correlations of the system. The transformation…
We propose a gauge-invariant system of the Chern-Simons-Schrodinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square…
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the…
We demonstrate that there exist stationary states of Bose-Einstein condensates in an optical lattice that do not satisfy the usual Bloch periodicity condition. Using the discrete model appropriate to the tight-binding limit we determine…