On calculation of vector spin chirality for zigzag spin chains

TL;DR

This paper calculates vector spin chirality in $S=1/2$ zigzag spin chains using DMRG, demonstrating chiral order and phase transitions, and compares results with theoretical predictions to map magnetic phases.

Contribution

It introduces a combined DMRG and unitary transformation method to analyze vector spin chirality in zigzag chains, confirming theoretical predictions and exploring phase diagrams.

Findings

Chiral order observed in zigzag XY chain.

Chirality correlation functions match bosonization analysis.

Magnetic phase diagram determined for $S=1/2$ zigzag Heisenberg chain.

Abstract

We calculate the vector spin chirality for $S=1/2$ zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the $S=1/2$ zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.