Linked-cluster expansions for quantum magnets on the hypercubic lattice

TL;DR

This paper uses high-order linked-cluster expansions to analyze quantum phase transitions in spin models on hypercubic lattices across various dimensions, providing precise phase boundary and critical exponent data.

Contribution

It introduces a systematic high-order linked-cluster expansion approach for quantum magnets on hypercubic lattices, including exact coefficients for the $1/d$ expansion of phase boundaries.

Findings

Determined phase transition points and critical exponents across dimensions.

Extracted coefficients of the $1/d$ expansion for phase boundaries.

Provided high-precision data for quantum phase transitions in spin models.

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.