Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

TL;DR

This study uses DMRG to analyze the ground states of frustrated spin-1/2 Heisenberg ladders, revealing a transition from dimerized to spin-liquid states as the number of legs increases, with implications for two-dimensional systems.

Contribution

It provides the first comprehensive DMRG analysis of frustrated $J_1-J_3$ Heisenberg ladders up to 8 legs, demonstrating the evolution from dimerized to spin-liquid ground states.

Findings

Finite spin gap in strong frustration regime.

Dimerized ground state on odd-leg ladders.

Exponential decay of dimer correlations on even-leg ladders.

Abstract

We present a Density Matrix Renormalization Group (DMRG) study of the ground-state properties of spin-1/2 frustrated $J_1-J_3$ Heisenberg $n_l$-leg ladders (with $n_l$ up to 8). For strong frustration ($J_3/J_1\simeq 0.5$), both even- and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.