Emergent Spin Excitations in a Bethe Lattice at Percolation

TL;DR

This study investigates how dilution-induced dangling spins in a Bethe lattice at percolation create emergent spin excitations, revealing their interactions and low-energy states through DMRG calculations.

Contribution

It demonstrates the existence and behavior of emergent spin 1/2 degrees of freedom in a diluted Bethe lattice, with an effective Hamiltonian describing their interactions.

Findings

Emergent spins are present at percolation threshold.

Interactions decay exponentially with distance.

Low-lying quasidegenerate states are identified.

Abstract

We study the spin 1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even/odd sublattice imbalance resulting in "dangling spins" (L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)). These collectively act as "emergent" spin 1/2 degrees of freedom and are responsible for the creation of a set of low lying "quasidegenerate states". Using Density Matrix Renormalization Group (DMRG) calculations, we detect the presence and location of these emergent spins. We find an effective Hamiltonian of these emergent spins, with Heisenberg interactions that decay exponentially with the distance between them.