March 6, 2000
We analyze the logarithmic corrections due to ferromagnetic impurity ending bonds of open spin 1/2 antiferromagnetic chains, using the density matrix renormalization group technique. A universal finite size scaling $\sim {\frac 1 {L \log L}}$ for impurity contributions in the quasi-degenerate ground state energy is demonstrated for a zigzag spin 1/2 chain at the critical next nearest neighbor coupling and the standard Heisenberg spin 1/2 chain, in the long chain limit. Using an exact solution for the latter case it is argued that one can extract the impurity contributions to the entropy and specific heat from the scaling analysis. It is also shown that a pure spin 3/2 open Heisenberg chain belongs to the same universality class.
Similar papers 1
June 27, 2000
The manifestations of topological effects in finite antiferromagnetic Heisenberg chains is examined by density matrix renormalization group technique in this paper. We find that difference between integer and half-integer spin chains shows up in ground state energy per site when length of spin chain is longer than $\sim\xi$, where $\xi\sim\exp(\pi S)$ is a spin-spin correlation length, for spin magnitude S up to 5/2. For open chains with spin magnitudes $S=5/2$ to S=5, we ver...
June 9, 2010
The effects of boundary impurities on the entanglement entropy in an antiferromagnetic Heisenberg opened spin-$1/2$ chain are investigated. The method of density-matrix renormalization-group is used to obtain the bipartite entanglement. The entropy increases when the length of the subsystem increases. It will approach to a constant when system length is very large. With the same impurity interaction, qutrit impurities of spin-$1$ can increase the entanglement entropy.
April 11, 2000
We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process($M$-$H$ curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization, susceptibi...
March 3, 2006
Using the DMRG method we calculate the surface spin correlation function, $C_L(l)=< S_l^z S_{L+1-l}^z>$, in the spin $S=3/2$ antiferromagnetic Heisenberg chain. For comparison we also investigate the $S=1/2$ chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, $C_L(1)\sim (\log L)^{-2d}$, with $d=0.13(2)$. We find no surface order, in clear contrast with the behavior of the...
October 7, 1998
Corrections to the asymptotic correlation function in a Heisenberg spin-1/2 antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a function of the distance r or the chain size L. This leads to significant differences with numerical results. We calculate the sub-leading logarithmic corrections to the finite-size correlation function, using renormalization group improved perturbation theory, and compare the result with numerical data.
October 10, 2003
We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundar...
July 4, 1998
We consider a magnetic impurity in the antiferromagnetic spin-1/2 chain which is equivalent to the two-channel Kondo problem in terms of the field theoretical description. Using a modification of the transfer-matrix density matrix renormalization group (DMRG) we are able to determine local and global properties in the thermodynamic limit. The cross-over function for the impurity susceptibility is calculated over a large temperature range, which exhibits universal data-collaps...
June 9, 2000
We study a spin 1/2 Heisenberg zigzag spin chain model near decoupled two chains. Taking into account a symmetry breaking perturbation, we discuss the existence of an energy gap in the ferromagnetic interchain coupling as well as the antiferromagnetic one. In the ferromagnetic model, a marginally relevant fixed line reduces the gap strongly, so that the correlation length becomes an astronomical length scale even in order 1 coupling. This result agrees with density matrix ren...
December 20, 1994
The $s=1$ Heisenberg Antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with $J'\ne J$ at the center of an even-length open chain is considered. Using the density matrix renormalization group method we find that, for sufficiently strong or weak $J'$, a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbati...
October 11, 1996
In this paper we study the finite size scaling for low energy excitations of $S=1$ and $S=2$ Heisenberg chains, using the density matrix renormalization group technique. A crossover from $1/L$ behavior (with $L$ as the chain length) for medium chain length to $1/L^2$ scaling for long chain length is found for excitations in the continuum band as the length of the open chain increases. Topological spin $S=1/2$ excitations are shown to give rise to the two lowest energy states ...