Related papers: Ordering of Energy Levels in Heisenberg Models and…

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…

We demonstrate a violation of the ``ferromagnetic ordering of energy levels'' conjecture (FOEL) for even length spin rings. The FOEL conjecture was a guess made by Nachtergaele, Spitzer and an author for the Heisenberg model on certain…

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…

We prove a result for the spin-$1/2$ quantum Heisenberg ferromagnet on $d$-dimensional boxes $\{1,\dots,L\}^d \subset \mathbb{Z}^d$. For any $n$, if $L$ is large enough, the Hamiltonian satisfies: among all vectors whose total spin is at…

The Lieb-Mattis theorem on the antiferromagnetic ordering of energy levels is generalized to SU(N) extended Hubbard model with Heisenberg exchange and pair-hopping terms. It is proved that the minimum energy levels among the states from…

Exact spectra of periodic samples are computed up to $ N=36 $. Evidence of an extensive set of low lying levels, lower than the softest magnons, is exhibited. These low lying quantum states are degenerated in the thermodynamic limit; their…

The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg…

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…

We introduce a new simple hierarchically constrained model of slow relaxation. The configurational energy has a simple form as there is no coupling among the spins defining the system; the associated stationary distribution is an…

The ordering of weakly coupled random antiferromagnetic $S=1/2$ chains, as relevant for recent experimentally investigated spin chain materials, is considered theoretically. The one-dimensional isotropic Heisenberg model with random…

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…

Ordering of the classical Heisenberg antiferromagnet on the triangular lattice is studied by means of a mean-field calculation, a scaling argument and a Monte Carlo simulation, with special attention to its vortex degree of freedom. The…

The ordering property of the classical pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbor interaction is investigated by means of a Monte Carlo simulation. The model is found to exhibit a first-order…

The 3$d$-electronic spin dynamics and the magnetic order in Fe$_3$PO$_4$O$_3$ were investigated by muon spin rotation and relaxation ($\mu$SR) and $^{57}$Fe M\"ossbauer spectroscopy. Zero-field (ZF)-$\mu$SR and $^{57}$Fe M\"ossbauer studies…

Heisenberg ladders are investigated using the bond-mean-field theory [M.Azzouz, Phys. Rev. B 48, 6136 (1993)]. The zero inter-ladder coupling energy gap, the uniform spin susceptibility and the nuclear magnetic resonance spin-relaxation…

We investigate properties of a spin-1 Heisenberg model with extended and biquadratic interactions, which captures crucial aspects of the low energy physics in FeSe. While we show that the model exhibits a rich phase diagram with four…

In models like axion monodromy, temporal features during inflation which are not associated with its ending can produce scalar, and to a lesser extent, tensor power spectra where deviations from scale-free power law spectra can be as large…

In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multi-spin $\text{U(1)}$ order…

We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in…