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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 ...
Let L be a lattice in . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in . The first method is based on the observation that if the sphere is sufficiently small then the la ...
The unique shortest vector problem on a rational lattice is the problem of finding the shortest non-zero vector under the promise that it is unique (up to multiplication by -1). We give several incremental improvements on the known hardness of the unique s ...
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 ...
By ab initio many-body quantum chemistry calculations, we determine the strength of the symmetric anisotropy in the 5d5 j ~ 1/2 layered material Ba2IrO4. While the calculated anisotropic couplings come out in the range of a few meV, orders of magnitude str ...
Motivated by some inconsistencies in the way quantum fluctuations are included beyond the classical treatment of hard-core bosons on a lattice in the recent literature, we revisit the large-S semiclassical approach to hard-core bosons on the square lattice ...
Iron based high temperature superconductors have several common features with superconducting cuprates, including the square lattice and the proximity to an antiferromagnetic phase. The magnetic excitation spectrum below T-c of Fe1.02Te0.7Se0.3 shows an ho ...
Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the ...
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 ...
Consider bond percolation on the square lattice Z(2) where each edge is independently open with probability p : For some positive constants p(0) is an element of( 0; 1); epsilon(1) and epsilon(2); the following holds: if p > p(0); then with probability at ...