No Arabic abstract
Linear Heisenberg antiferromagnets (HAFs) are chains of spin-$S$ sites with isotropic exchange $J$ between neighbors. Open and periodic boundary conditions return the same ground state energy in the thermodynamic limit, but not the same spin $S_G$ when $S ge 1$. The ground state of open chains of N spins has $S_G = 0$ or $S$, respectively, for even or odd N. Density matrix renormalization group (DMRG) calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities $rho(r,N)$ of edge states in HAFs with $S = 1$, 3/2 and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $rho(r,N)propto(-1)^{r-1}$ for $r=1,2,ldots N$. The SDWs are in phase when N is odd, out of phase when N is even, and have finite excitation energy $Gamma(N)$ that decreases exponentially with N for integer $S$ and faster than 1/N for half integer $S$. The spin densities and excitation energy are quantitatively modeled for integer $S$ chains longer than $5 xi$ spins by two parameters, the correlation length $xi$ and the SDW amplitude, with $xi = 6.048$ for $S = 1$ and 49.0 for $S = 2$. The BI-SDWs of $S = 3/2$ chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases $|Gamma(N)|$ and weakens the size dependence. The nonlinear sigma model (NL$sigma$M) has been applied the HAFs, primarily to $S = 1$ with even N, to discuss spin densities and exchange between localized states at the ends as $Gamma(N) propto (-1)^N exp(-N/xi)$...
Using (infinite) density matrix renormalization group techniques, ground state properties of antiferromagnetic S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid as well as the spin-liquid and the ferromagnetic phases. Analyzing spin correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.
We report zero and longitudinal magnetic field muon spin relaxation measurements of the spin S=1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B the spin-lattice relaxation rate follows a power law B^n with n=-0.9(3). This result is temperature independent for 5K < T < 300 K. Within conformal field theory and using the Muller ansatz we conclude ballistic spin transport in SrCuO2.
We report on inelastic neutron scattering (INS) measurements on the molecular spin ring CsFe$_8$, in which eight spin-5/2 Fe(III) ions are coupled by nearest-neighbor antiferromagnetic Heisenberg interaction. We have recorded INS data on a non-deuterated powder sample up to high energies at the time-of-flight spectrometers FOCUS at PSI and MARI at ISIS, which clearly show the excitation of spin waves in the ring. Due to the small number of spin sites, the spin-wave dispersion relation is not continuous but quantized. Furthermore, the system exhibits a gap between the ground state and the first excited state. We have modeled our data using exact diagonalization of a Heisenberg-exchange Hamiltonian together with a small single-ion anisotropy term. Due to the molecules symmetry, only two parameters $J$ and $D$ are needed to obtain excellent agreement with the data. The results can be well described within the framework of the rotational-band model as well as antiferromagnetic spin-wave theories.
The quantum entanglement measure is determined, for the first time, for antiferromagnetic trimer spin-1/2 Heisenberg chains. The physical quantity proposed to measure the entanglement is the distance between states by adopting the Hilbert-Schmidt norm. The method is applied to the new magnetic Cu(II) trimer system, 2b.3CuCl_2.2H_2O, and to the trinuclear Cu(II) halide salt, (3MAP)_2Cu_2Cl_8. The decoherence temperature, above which the entanglement is suppressed, is determined for the both systems. A correlation among their decoherence temperatures and their respective exchange coupling constants is established.
An efficient density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity $Z = 3$ and antiferromagnetic exchange between nearest neighbor spins $s= 1/2$ or 1 sites in successive generations $g$. The algorithm is accurate for $s = 1$ sites. The ground states are magnetic with spin $S(g) = 2^g s$, staggered magnetization that persists for large $g > 20$ and short-range spin correlation functions that decrease exponentially. A finite energy gap to $S > S(g)$ leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for $s$ = 1/2 and 1 are interpreted in terms of an analytical three-site model.