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arXiv · 1605.05848

Linked-cluster expansions for quantum magnets on the hypercubic lattice

K. Coester·D. G. Joshi·M. Vojta·K. P. Schmidt
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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 $ν$ 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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K. Coester, D. G. Joshi, M. Vojta, K. P. Schmidt. 2016-05-19. Linked-cluster expansions for quantum magnets on the hypercubic lattice. https://doi.org/10.1103/physrevb.94.125109

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