Linked-cluster expansions for quantum magnets on the hypercubic lattice

Abstract

For arbitrary space dimension $d$ we investigate the quantum phase transitions of two paradigmatic spin models defined on a hypercubic lattice, the coupled-dimer Heisenberg model and the transverse-field Ising model. To this end high-order linked-cluster expansions for the ground-state energy and the one-particle gap are performed up to order 9 about the decoupled-dimer and high-field limits, respectively. Extrapolations of the high-order series yield the location of the quantum phase transition and the correlation-length exponent $\nu$ as a function of space dimension $d$. The results are complemented by $1/d$ expansions to next-to-leading order of observables across the phase diagrams. Remarkably, our analysis of the extrapolated linked-cluster expansion allows to extract the coefficients of the full $1/d$ expansion for the phase-boundary location in both models exactly in leading order and quantitatively for subleading corrections.

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• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets II: Antiferromagnetic phase and quantum phase transition
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• High-order series expansion of non-Hermitian quantum spin models
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Linked Cluster Expansions via Hypergraph Decompositions
• Dynamic structure factor of Heisenberg bilayer dimer phases in the presence of quenched disorder and frustration
• Deep learning nonlocal and scalable energy functionals for quantum Ising models