Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice

TL;DR

This paper advances the modified spin-wave theory by optimizing the ordering vector to better describe frustrated bosons on an anisotropic triangular lattice, revealing complex phase diagrams and finite-temperature behaviors.

Contribution

It introduces an improved MSW approach with ordering vector optimization, providing accurate phase diagrams and insights into quantum and thermal phase transitions in frustrated boson systems.

Findings

MSW results agree with ED and PEPS calculations at zero temperature.

Identifies multiple phases including 1D quasi-ordered, Neel, and spiraling ordered phases.

Finite temperature analysis shows transition from long-range order to quasi-order and short-range correlations.

Abstract

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D spiraling ordered phase. We have strong indications that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory we also explore the finite-temperature phase diagram. We find that the zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that modified spin-wave theory is very well suited for describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast method for singling out Hamiltonians which may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator.