Gapless points of dimerized quantum spin chains: analytical and numerical studies

TL;DR

This paper investigates the precise locations of gapless points in finite quantum spin chains with dimerization, comparing analytical tunneling and matrix element calculations with numerical diagonalization results across different spin values.

Contribution

It introduces analytical methods for identifying gapless points and compares them with numerical results, highlighting discrepancies and raising questions about existing tunneling approximations.

Findings

Numerical diagonalization aligns well with Neel state calculations.

Tunneling results differ significantly from other methods for strong dimerization.

Discrepancies suggest possible corrections to tunneling approximations.

Abstract

We study the locations of the gapless points which occur for quantum spin chains of finite length (with a twisted boundary condition) at particular values of the nearest neighbor dimerization, as a function of the spin S and the number of sites. For strong dimerization and large values of S, a tunneling calculation reproduces the same results as those obtained from more involved field theoretic methods using the non-linear sigma-model approach. A different analytical calculation of the matrix element between the two Neel states gives a set of gapless points; for strong dimerization, these differ significantly from the tunneling values. Finally, the exact diagonalization method for a finite number of sites yields a set of gapless points which are in good agreement with the Neel state calculations for all values of the dimerization, but the agreement with the tunneling values is not very good even for large S. This raises questions about possible corrections to the tunneling results.