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

TL;DR

This paper investigates quantum tricriticality in an incommensurate phase of a frustrated Ising magnet, revealing how quantum strings and long-range interactions induce complex phase transitions.

Contribution

It introduces a detailed analysis of quantum tricriticality driven by effective long-range inter-string interactions in a frustrated Ising model.

Findings

Incommensurate phase stabilized by spatial anisotropy.

Linear relationship between incommensurate wave vector and string density.

Identification of a quantum tricritical point due to competing long-range interactions.

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 the large scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate 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 interaction, 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.