Quantum tricriticality of incommensurate phase induced by quantum strings in frustrated Ising magnetism

Abstract

Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as "quantum strings". Here we study an extended transverse field Ising model on a triangular lattice. Using large-scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommen-surate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in under-doped cuprate superconductors. When introducing the next-nearest-neighbor in-teraction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is non-trivially caused by effective long-range inter -string interactions with two competing terms following different decaying behaviors.