Systematic analysis of crystalline phases in bosonic lattice models with algebraically decaying density-density interactions

Abstract

We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying density-density interactions on arbitrary lattices. The key idea is a systematic search for the energetically best order on all unit cells of the lattice up to a given extent. Using resummed couplings we evaluate the energy of the ordering patterns in the thermodynamic limit using finite unit cells. We apply the proposed approach to the atomic limit of the extended Bose-Hubbard model on the triangular lattice at fillings f=1/2f=1/2 and f=1f=1. We investigate the ground-state properties of the antiferromagnetic long-range Ising model on the triangular lattice and determine a six-fold degenerate plain-stripe phase to be the ground state for finite decay exponents. We also probe the classical limit of the Fendley-Sengupta-Sachdev model describing Rydberg atom arrays. We focus on arrangements where the atoms are placed on the sites or links of the Kagome lattice. Our method provides a general framework to treat cristalline structures resulting from long-range interactions.

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

“…Then, one would not have to account for the coordination number q and the number of monomorphism would be larger by a factor of q, making it computationally more expensive. In the end, we obtain the ground-state energy (per site) as a high-order perturbative series in an expansion parameter λ up to a computationally feasible maximal order o max as in Equation (110). 1qp dispersion: We now turn to the one-quasiparticle channel and calculate the hopping amplitudes.…”

“…For the first part of this section, we review the antiferromagnetic LRTFIM on the triangular lattice [27,29,30,32,40,110,277]. In the nearest-neighbour limit of that model, the zero-field case has an extensively degenerate ground state [268,270,271,273].…”

“…To infer the nature of the full phase diagram including the transverse field and the long-range interaction, the next step is to discuss the zero-field limit of the Ising model with long-range interactions. As the antiferromagnetic long-range interactions introduce a hierarchy of constraints due to the interaction between sites further apart, the longrange interaction breaks the ground-state degeneracy of the nearest-neighbour zero-field as well [30,110,277,279]. It is important to emphasise that the long-range interaction lifts the degeneracy in a different way and stabilises a gapped stripe phase breaking the translational symmetry in a different way than the clock order promoted by the transverse field [30,110,277,279,280].…”

“…As the antiferromagnetic long-range interactions introduce a hierarchy of constraints due to the interaction between sites further apart, the longrange interaction breaks the ground-state degeneracy of the nearest-neighbour zero-field as well [30,110,277,279]. It is important to emphasise that the long-range interaction lifts the degeneracy in a different way and stabilises a gapped stripe phase breaking the translational symmetry in a different way than the clock order promoted by the transverse field [30,110,277,279,280]. This plain stripe state is sixfold degenerate by rotations around π/3, as well as spin flips [30,110,277,279].…”

“…Further, QPTs in systems with competing long-range interactions do not tend to depend on the long-range nature of the interaction [23][24][25][26]29,30,32]. In several cases, long-range interactions then lead to the emergence of ground states and QPTs, which are not present in the corresponding short-range interacting models [27,30,54,55,[109][110][111][112].…”