Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain

TL;DR

This paper investigates the boundary spin correlations in the S=3/2 antiferromagnetic Heisenberg chain, revealing a logarithmic delocalization of end spins and contrasting it with integer spin chains.

Contribution

It demonstrates that end spins in half-integer spin chains are weakly delocalized with logarithmic decay, challenging the notion of strict end spins and supporting universality in boundary behavior.

Findings

End-to-end correlations decay logarithmically as (log L)^{-2d}

No surface order is observed in half-integer spin chains

The first energy gap vanishes as (π v_S d)/(L log L)

Abstract

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 S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as $\Delta_1 \approx (\pi v_S d)/(L\ln L)$, where $v_S$ is the sound velocity and $d$ is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.