Linked-cluster expansions for quantum magnets on the hypercubic lattice

2016/05/19 by K. Coester, Darshan G. Joshi, D. G. Joshi +4
Physics and Astronomy · #Cluster expansion #Ground state #Ising model #Lattice (music) #Mathematical physics #Observable #Phase space #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Theoretical and Computational Physics #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.94.125109

published as Phys. Rev. B 94, 125109 (2016)

arxiv created 2016/05/19 · openalex publication_date 2016/09/06 · arxiv updated 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 \ensuremathν 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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