Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance

TL;DR

This paper investigates the low-energy spectrum of a spin-1/2 Heisenberg antiferromagnet on Cayley trees, revealing the role of sublattice imbalance and identifying giant spin degrees of freedom through numerical and analytical methods.

Contribution

It introduces a DMRG approach for tree graphs, uncovers low-energy states related to sublattice imbalance, and generalizes mean-field theory to nonuniform lattices.

Findings

Discovery of quasidegenerate low-energy states on Cayley trees

Identification of giant spins arising from sublattice imbalance

Analytical understanding of finite-size spin gap scaling

Abstract

To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.