Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet

TL;DR

This paper maps the phase diagram of a breathing frustrated J1-J2 Heisenberg model, revealing ordered phases and a higher-order topological quantum magnet state, with topological spinon corner modes emerging from the system.

Contribution

It introduces a comprehensive phase diagram of the breathing frustrated J1-J2 Heisenberg model, identifying topological quantum magnetism and associated topological modes using advanced many-body methods.

Findings

First order transition between stripe order and topological quantum magnet

Second order transition between Neel order and quantum magnet

Emergence of topological spinon corner modes

Abstract

Competing interactions in quantum magnets lead to a variety of emergent states, including ordered phases, nematic magnets and quantum spin liquids. Among them, topological quantum magnets represent a promising platform to create topological excitations protected by the bulk many-body excitation gap. Here we establish the phase diagram of a breathing frustrated antiferromagnetic J1-J2-Heisenberg model, featuring both ordered states and a higher-order topological quantum magnet state. Using exact many-body methods based on neural network quantum states and tensor networks, we determine the existence of a first order phase transition between stripe order and the topological quantum magnet and the second order phase transition between the Neel order and quantum magnet phase, further corroborated by calculations of the many-body gap. Using an auxiliary fermion parton formalism, we show the emergence of topological spinon corner modes stemming from the breathing order parameter of the parent Heisenberg model. Our results establish the breathing frustrated square lattice Heisenberg model as a paradigmatic system to engineer topological quantum magnetism, as recently realized in Ti lattices at MgO.