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 one-dimensional (1D) quasi-ordered phase, a 2D Néel ordered phase and a 2D spiraling ordered phase. Strong indications coming from the ED and PEPS calculations, as well as from the breakdown of MSW theory, suggest 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. In agreement with the Berezinskii–Kosterlitz–Thouless (BKT) theory, we find that zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a BKT transition temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that, despite its simplicity, MSW theory is very well suited to 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 and reliable method for singling out Hamiltonians that 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 instead of theoretical methods.
Highlights
Lattice models of strongly interacting bosons have recently been implemented experimentally thanks to impressive developments with trapped ultra-cold atoms in optical lattice potentials [1, 2]
XY antiferromagnets can be regarded as the limiting case of antiferromagnetic Hamiltonians with planar anisotropy in the couplings, relevant to the description of frustrated antiferromagnetic materials, and they can describe the physics of Cooper pairs in arrays of ultra-small Josephson junctions with magnetic frustration [10]
More recently we have proposed that frustrated XY antiferromagnets can be experimentally implemented by loading planarly trapped ions into an optical lattice [11]
Summary
Lattice models of strongly interacting bosons have recently been implemented experimentally thanks to impressive developments with trapped ultra-cold atoms in optical lattice potentials [1, 2]. In this work we focus on a triangular lattice with antiferromagnetic nearest-neighbor interactions, which can be seen as a ferromagnetic lattice (tij > 0) with half a magnetic flux quantum threaded through each lattice plaquette This magnetic flux can, for instance, be interpreted as flipping the signs of all hopping amplitudes of the bonds along the horizontal direction of the lattice (Fig. 1). The aim of this work is the determination of the ground-state and finite-temperature phase diagrams of the S = 1/2 XY antiferromagnet (AF) - or, alternatively, of frustrated half-filled hardcore bosons - on a spatially anisotropic triangular lattice (SATL) by means of spin-wave theory.
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