Composite Boson Mapping for Lattice Boson Systems

Abstract

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into $2\times 2$ composite bosons and solve it at mean field. The resulting Mott insulator-superfluid phase diagram reproduces well Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole symmetry line is unraveled and in remarkable agreement with experiment. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.

8 pages, 4 figures

References in corpus (7)

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• Monte Carlo study of two-dimensional Bose-Hubbard model
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• Density-dependent synthetic magnetism for ultracold atoms in optical lattices
• The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields
• A case study of spin-$1$ Heisenberg model in a triangular lattice
• Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint
• Quantum Gutzwiller approach for the two-component Bose-Hubbard model
• Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Extended Bose Hubbard model for two leg ladder systems in artificial magnetic fields
• Cluster Gutzwiller study of Bose-Hubbard ladder: ground-state phase diagram and many-body Landau-Zener dynamics
• A generalized perspective on non-perturbative linked cluster expansions
• Bosonic self-energy functional theory
• Quantum phases of constrained dipolar bosons in coupled one-dimensional optical lattices
• Two supersolid phases in hard-core extended Bose-Hubbard model
• Quantum phases of constrained bosons on a two-leg Bose-Hubbard ladder
• Emergent magnetic order in the antiferromagnetic Kitaev model with a [111] field
• Cluster Mean-Field Signature of Entanglement Entropy in Bosonic Superfluid-Insulator Transitions
• Variational Quantum Simulation of Valence-Bond Solids
• Composite fermion-boson mapping for fermionic lattice models
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Twisted superfluid and supersolid phases of triplons in bilayer honeycomb magnets