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arXiv:hep-th/0506171 · Letters in Mathematical Physics

Density Matrix of a Finite Sub-chain of the Heisenberg Anti-ferromagnet

H. Boos, M. Jimbo, T. Miwa, Fedor Aleksandrovich Smirnov, Y. Takeyama

Published Feb 16, 2006• 44 citations
arXivHTMLPDF
DOI
10.1007/s11005-006-0054-x

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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 $\ensuremath{\sim}1/(L\mathrm{ln}L)$ for impurity contributions in the quasidegenerate 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.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.