Antiferromagnetic Heisenberg ladders in a staggered magnetic field

TL;DR

This paper investigates how a staggered magnetic field affects low-energy excitations in antiferromagnetic Heisenberg chains and ladders, revealing gap formation and scaling behaviors with increasing ladder width.

Contribution

It introduces a modified boundary scheme to accurately analyze bulk excitations and determines the field scaling exponent for the gaps in multi-leg ladders.

Findings

Staggered magnetic field induces gaps and midgap states in chains and ladders.

Gap values converge quickly with increasing ladder width, indicating a universal scaling exponent.

Midgap states share the same scaling exponents as bulk gaps, but their large-N behavior requires further study.

Abstract

We study the low-energy excitations of the spin-1/2 antiferromagnetic Heisenberg chain and $N$-leg ($N$=2, 3, 4) ladders in a staggered magnetic field $h_s$. We show that $h_s$ induces gap and midgap states in all the cases and examine their field scaling behavior. A modified boundary scheme is devised to extract accurate bulk excitation behavior. The gap values converge rapidly as $N$ increases, leading to a field scaling exponent $\gamma=1/2$ for both the longitudinal and transverse gaps of the square lattice ($N \to \infty$). The midgap states induced by the boundary edge effects share the bulk gap scaling exponents but their overall scaling behavior in the large-N limit needs further investigation.