Ground states of a J-Q model with long-range antiferromagnetic interactions

We employ large-scale sign-free quantum Monte Carlo and Lanczos exact diagonalization to study the 1D J-Q model (a Heisenberg antiferromagnetl with multi-spin couplings added) with long-range interactions. Three phases, an ordered anti-ferromagnet (AFM), a quasi long-range ordered (QLRO state), and a valence bond solid (VBS), are identified by applying Binder-cumulant and level-crossing methods. We investigate different characteristics of these phases and their quantum phase transitions. From our numerical data and for the model we studied, the Binder-cumulant method has advantages in determining the quantum critical AFM-QLRO point and a certain range of the QLRO-VBS transition line, while the level crossing method is more suitable for the other region of QLRO-VBS transition. In addition, there could be a direct quantum phase transition between the AFM and VBS phases, possibly an analog of the 2D deconfined quantum critical point (DQCP) in one dimension.