Scaling of excitations in dimerized and frustrated spin-1/2 chains

TL;DR

This paper investigates how low-lying excitations in dimerized and frustrated spin-1/2 chains scale with system size, using numerical methods to compare with theoretical models and identify regimes of agreement.

Contribution

It provides a detailed numerical analysis of excitation scaling in spin chains with dimerization and frustration, confirming theoretical predictions and identifying regimes of good agreement.

Findings

Elementary excitations show clear scaling behavior over a wide range of system sizes.

At the critical frustration point, numerical results match sine-Gordon model predictions without logarithmic corrections.

Good agreement with theoretical models for small dimerization parameters at sufficiently large chain lengths.

Abstract

We study the finite-size behavior of the low-lying excitations of spin-1/2 Heisenberg chains with dimerization and next-to-nearest neighbors interaction, J_2. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results, and shows that, for different values of the dimerization parameter \delta, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of \ell=L/\xi (where L is the length of the chain and \xi is the correlation length). At J_2=J_2c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luscher's theory. For small \delta we find a very good agreement for \ell > 4 or 7 depending on the excitation considered.