Ground-state phase diagram of the frustrated spin-1/2 two-leg honeycomb ladder

TL;DR

This study maps the complex phase diagram of a frustrated spin-1/2 honeycomb ladder, revealing five distinct phases and analyzing the nature of phase transitions using advanced numerical and analytical methods.

Contribution

It provides the first comprehensive phase diagram of the frustrated honeycomb ladder, identifying new phases and characterizing the critical behaviors of phase transitions.

Findings

Identified five distinct quantum phases in the model.

Discovered reentrant behavior of the dimerized phase.

Characterized phase transitions with specific universality classes.

Abstract

We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two $J_1$-$J_2$ spin chains coupled with $J_\perp$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: A Haldane phase, a NNN-Haldane phase and a staggered dimer phase when $J_{\perp} < 0$; a rung singlet phase and a columnar dimer phase when $J_{\perp} > 0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration $J_2$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with central charge $c=1/2$. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has central charge $c=2$.