Gapless Spin Liquid and Non-local Corner Excitation in the Spin-1/2 Heisenberg Antiferromagnet on Fractal

TL;DR

This paper investigates a spin-1/2 Heisenberg antiferromagnet on a fractal Sierpiński gasket, revealing a gapless spin liquid state with non-local excitations and long-range entanglement, advancing understanding of quantum states in fractal geometries.

Contribution

It demonstrates the existence of a gapless spin liquid and non-local corner excitations in a fractal spin system using tensor network methods, a novel exploration of quantum states in fractal structures.

Findings

Identified a gapless spin-liquid ground state.

Discovered non-local corner excitations.

Showed long-range entanglement despite short-range correlations.

Abstract

Motivated by the mathematical beauty and the recent experimental realizations of fractal systems, we study the spin-$1/2$ antiferromagnetic Heisenberg model on a Sierpi\'nski gasket. The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states. Using advanced tensor network techniques, we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension. This fractal spin system also demonstrates nontrivial non-local properties. While the extremely short-range correlation causes a highly degenerate spin form factor, the entanglement in this fractal system suggests a long-range scaling behavior. We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement. Our results unambiguously point out multiple essential properties of this fractal spin system, and open a new route to explore spin liquid and frustrated magnetism.