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 $f=1/2$ and $f=1$. 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. \changed{Our method provides a general framework to treat cristalline structures resulting from long-range interactions.

35 pages, 11 figures

References in corpus (26)

• Many-Body Physics with Ultracold Gases
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Statistical mechanics and dynamics of solvable models with long-range interactions
• An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Supersolid hardcore bosons on the triangular lattice
• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Competing density-wave orders in a one-dimensional hard-boson model
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• New frontiers with quantum gases of polar molecules
• Quantum phases of Rydberg atoms on a kagome lattice
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Metastable states of a gas of dipolar bosons in a 2D optical lattice
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Observing emergent hydrodynamics in a long-range quantum magnet
• Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
• Finite-range interacting Ising quantum magnets with Rydberg atoms in optical lattices - From Rydberg superatoms to crystallization
• Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice
• Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• Scaling at quantum phase transitions above the upper critical dimension
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Supersolid phases of ultracold bosons trapped in optical lattices dressed with Rydberg $p$-states
• Quantum phases of dipolar bosons in one-dimensional optical lattices
• Supersolid phases of Rydberg-excited bosons on a triangular lattice
• Continuously varying critical exponents in long-range quantum spin ladders

Cited by in corpus (6)

• Monte Carlo based techniques for quantum magnets with long-range interactions
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Observation of Unprecedented Fractional Magnetization Plateaus in a New Shastry-Sutherland Ising Compound
• Fractal ground state of ion chains in periodic potentials
• Quantum frustrated Wigner chains
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators