Frustration-induced quantum spin liquid behavior in the $s=$1/2 random-bond Heisenberg antiferromagnet on the zigzag chain

TL;DR

This study investigates how frustration and randomness induce a quantum spin liquid-like state in a one-dimensional $s=1/2$ Heisenberg model, revealing a phase transition between unfrustrated and frustrated random-singlet states with distinct thermodynamic behaviors.

Contribution

It uncovers a transition from an unfrustrated to a frustrated random-singlet state in a 1D quantum magnet, elucidating the nature of randomness-induced quantum spin liquids in low dimensions.

Findings

Frustration causes a phase transition to a different gapless nonmagnetic state.

The frustrated RS state exhibits $T$-linear specific heat similar to higher-dimensional QSLs.

Unfrustrated RS state shows a $rac{1}{( ext{log} T)^3}$ low-temperature specific heat.

Abstract

Recent studies have revealed that the randomness-induced quantum spin liquid (QSL)-like state is stabilized in certain frustrated quantum magnets in two and three dimensions. In order to clarify the nature of this gapless QSL-like state, we investigate both zero- and finite-temperature properties of the random-bond one-dimensional (1D) $s=12$ Heisenberg model with the competing nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by means of the exact diagonalization, density-matrix renormalization-group and Hams--de Raedt methods. We find that, on increasing the frustration $J_2$, the gapless nonmagnetic state stabilized in the unfrustrated model with $J_2=0$, the {\it unfrustrated\} random-singlet (RS) state, exhibits a phase transition into different gapless nonmagnetic state, the {\it frustrated\} RS state. This frustrated RS state in 1D has properties quite similar to the randomness-induced QSL-like state recently identified in 2D and 3D frustrated magnets exhibiting the $T$-linear low-temperature ($T$) specific heat, while the unfrustrated RS state is more or less specific to the unfrustrated 1D system exhibiting the $\sim 1(\log T)^3$ low-$T$ specific heat. Universal features and the robustness against perturbations of the frustrated RS state are emphasized.