We present a quantum Monte Carlo study for the isotropic antiferromagnetic Heisenberg chain coupled to Einstein phonons. By investigating the behavior of the correlation length we find the critical exponent to depend on both the phonon frequency and the spin-phonon coupling constant. Hence, these systems change the universality class continuously with the spin-phonon coupling.

Mar 11, 20190 citations

APS

Critical behavior of the S=3/2 Heisenberg chain

Adriana Moreo, K. Hallberg, Peter Horsch

Published Mar 1, 1996• 0 citations

OpenAlex

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Using the density-matrix renormalization group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to

s=9/2

. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly

c

, the sound velocity

{v}_{s}

, the anomalous dimension

{x}_{bulk}

, and the surface exponent

{x}_{s}

of the anisotropic spin-

s

Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entropy

S(L,{l}_{A},s)

of the spin-

s

Heisenberg chains satisfies the relation $S(L,{l}_{A},s)\ensuremath{-}S(L,{l}_{A},s\ensuremath{-}1)=1/(2s+1)$ for

s>3/2

in the thermodynamic limit.

Using the density-matrix renormalization-group technique we study the long-wavelength properties of the spin

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2

nearest-neighbor Heisenberg chain. We obtain an accurate value for the spin velocity $v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.87\ifmmode\pm\else\textpm\fi{}0.02$, in agreement with experiment. Our results show conclusively that the model belongs to the same universality class as the

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

Heisenberg chain, with a conformal central charge

c\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

and critical exponent $\ensuremath{\eta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.