Quantum versus classical behavior in the boundary susceptibility of the ferromagnetic Heisenberg chain

TL;DR

This paper investigates the boundary susceptibility of the quantum ferromagnetic Heisenberg chain, revealing quantum corrections to classical behavior and confirming results with numerical methods, with implications for experiments.

Contribution

It provides a modified spin-wave theory calculation of boundary susceptibility, highlighting quantum corrections and validating results with DMRG data.

Findings

Boundary susceptibility diverges as -T^{-3} at low temperatures.

Quantum corrections modify classical boundary susceptibility results.

Results agree with numerical DMRG data for S=1/2.

Abstract

We calculate the temperature dependence of the boundary susceptibility $\chi_B$ for the quantum ferromagnetic Heisenberg chain by a modified spin-wave theory (MSWT). We find that $\chi_B$ diverges at low temperatures $\sim -T^{-3}$ and therefore more rapidly and with opposite sign than the bulk susceptibility $\chi_{\text{bulk}}\sim T^{-2}$. Our result for $\chi_B$ is identical in leading order with the result for the classical system. In next leading orders, however, quantum corrections to the classical result exist which are important to obtain a good description over a wide temperature range. For the $S=1/2$ case, we show that our full result from MSWT is in excellent agreement with numerical data obtained by the density-matrix renormalization group applied to transfer matrices. Finally, we discuss the quantum to classical crossover as well as consequences of our results for experiment in some detail.