Related papers: Ordering of Energy Levels for Extended SU(N) Hubba…
The SU(n) symmetric antiferromagnetic finite chain with the fundamental representation and nearest-neighbor interaction is studied. A partial ordering between the lowest energy levels e(Y) in multiplet sectors corresponding to different…
The Lieb-Mattis theorem about antiferromagnetic ordering of energy levels on bipartite lattices is generalized to finite-size two-leg spin-1/2 ladder model frustrated by diagonal interactions. For reflection-symmetric model with…
The Lieb-Mattis theorem is generalized to an antiferromagnetic spin-ladder model with four-spin cyclic exchange interaction. We prove that for J>2K, the antiferromagnetic ordering of energy levels takes place separately in two sectors,…
Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions. We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species in the…
We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the Lieb-Mattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each…
We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains of any spin and XXZ spin chains with all spins equal to 1/2. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin…
Based on the exact solution of one-dimensional Fermi gas systems with $SU(n)$ symmetry in a hard wall, we demonstrate that we are able to sort the ordering of the lowest energy eigenvalues of states with all allowed permutation symmetries,…
The Heisenberg ferromagnet has symmetry group ${\rm SU}(2)$. The property known as ferromagnetic ordering of energy levels (FOEL) states that the minimum energy eigenvalue among eigenvectors with total spin $s$ is monotone decreasing as a…
The staggered magnetization of the Heisenberg antiferromagnet in two dimensions can be systematically approximated by a 1/N expansion. Cancellation between self energy diagrams leads to a Luttinger-like theorem for the ground state. We…
We use fermion mean field theory to study possible plaquette ordering in the antiferromagnetic SU(4) Heisenberg model. We find the ground state for both the square and triangular lattices to be the disconnected plaquette state. Our mean…
Consider a one-dimensional system of \( N \) electrons subject to an external potential \( U \). Let \( E_{\rm el}(S) \) denote the ground state energy of the system with total spin \( S \). The Mattis--Lieb theorem asserts that, for a…
We consider the class of quantum spin chains with arbitrary $U_q(\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\textrm{SU}_q(2)$ for the quantum deformation of $\textrm{SU}(2)$, for $q>0$. We derive sufficient…
For the frustrated two-dimensional $S=1/2$ antiferromagnetic Heisenberg model close to quantum phase transition we consider the singlet ground states retaining both translational and SU(2) symmetry. Besides usually discussed checkerboard,…
The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of…
The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P(U_i) = (1-f)\delta(U_i-U) + f\delta(U_i), is studied using a finite temperature quantum Monte Carlo technique and dynamical mean-field theory. We find…
We study the attractive SU($N$) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites $N_A$ $(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to identify the…
Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-$p$ symmetric ones with $p$ not a multiple of 3, it was argued that the…
We study the extended Hubbard model on a two-dimensional half-filled square lattice using the dynamical cluster approximation. We present results on the phase boundaries between the paramagnetic metallic (normal) state and the insulating…
The short ranged antiferromagnetism recently seen in UPt_3 is proved incompatible with two dimensional (2D) order parameter models that take the antiferromagnetism as a symmetry breaking field. To adjust to the local moment direction, the…
We explore the physics of the anisotropic compass model under the influence of perturbing Heisenberg interactions and present the phase diagram with multiple quantum phase transitions. The macroscopic ground state degeneracy of the compass…