Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...
The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on ...
We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...
We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate 6 representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) sym ...
We study the Neel to fourfold columnar valence bond solid (cVBS) quantum phase transition in a sign-free S = 1 square-lattice model. This is the same kind of transition that for S = 1/2 has been argued to realize the prototypical deconfined critical point. ...
Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...
The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF) analysis of both X-ray ...
Hexagonal lattice systems (e.g., triangular, honeycomb, kagome) possess a multidimensional irreducible representation corresponding to d(x2-y2) and d(xy) symmetry. Consequently, various unconventional phases that combine these d-wave representations can oc ...
We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find that (1) as a function of increasing nematicity, start ...
We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N = 3) and the checkerboard lattice (for N = 4), which are the line graphs of the honeycomb and square lattices and thus ...
We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group and infinite projected entangled-pair states. For the triangular lattice we confir ...
We provide strong evidence that the S = 1 bilinear-biquadratic Heisenberg model with nearest-neighbor interactions on the square lattice possesses an extended three-sublattice phase induced by quantum fluctuations for sufficiently large biquadratic interac ...
We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. No general analytical method to find a ground state exists when the spin dependence of the Hamiltonian is more than quadratic (i.e., beyond the Heisenberg model) ...
We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimens ...
Dislocations alter perfect crystalline order and produce anisotropic broadening of the X-ray diffraction profiles, which is described by the dislocation contrast factor. Owing to the lack of suitable mathematical tools to deal with dislocations in crystals ...
We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. On the basis of an algorithmic idea by Henley, we simulate a s ...
We investigate the properties of a two-dimensional frustrated quantum antiferromagnet on a square lattice, especially at infinitesimal doping. We find that next nearest neighbour (NN) J2 and next–next NN J3 interactions together destroy the antiferromagnet ...
The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an ...
We investigate the consequences of correlated hopping on the ground state properties of hard-core bosons on a square lattice as revealed by extensive exact diagonalizations and quantum Monte Carlo simulations. While for noninteracting hard-core bosons the ...
A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (N.Y.) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at finite doping whi ...
