Jan A. Koziol, Antonia Duft, Giovanna Morigi, Kai P. Schmidt
SciPost Phys. 14, 136 (2023) ·
published 30 May 2023

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We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying densitydensity interactions on arbitrary lattices. The key idea is a systematic search for the energetically best order on all unit cells of the lattice up to a given extent. Using resummed couplings we evaluate the energy of the ordering patterns in the thermodynamic limit using finite unit cells. We apply the proposed approach to the atomic limit of the extended BoseHubbard model on the triangular lattice at fillings $f=1/2$ and $f=1$. We investigate the groundstate properties of the antiferromagnetic longrange Ising model on the triangular lattice and determine a sixfold degenerate plainstripe phase to be the ground state for finite decay exponents. We also probe the classical limit of the FendleySenguptaSachdev model describing Rydberg atom arrays. We focus on arrangements where the atoms are placed on the sites or links of the Kagome lattice. Our method provides a general framework to treat cristalline structures resulting from longrange interactions.
A. Langheld, J. A. Koziol, P. Adelhardt, S. C. Kapfer, K. P. Schmidt
SciPost Phys. 13, 088 (2022) ·
published 10 October 2022

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The hyperscaling relation and standard finitesize scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension following the recently introduced QFSS formalism for thermal phase transitions. Contrary to longstanding belief, the correlation sector is affected by dangerous irrelevant variables. The presented formalism recovers a generalized hyperscaling relation and FSS form. Using this new FSS formalism, we determine the full set of critical exponents for the longrange transversefield Ising chain in all criticality regimes ranging from the nearestneighbor to the longrange mean field regime. For the same model, we also explicitly confirm the effect of dangerous irrelevant variables on the characteristic length scale.
Submissions
Submissions for which this Contributor is identified as an author:
Mr Koziol: "# Response: Anonymous Report 3..."
in Submissions  submission on Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying DensityDensity Interactions by J. A. Koziol, A. Duft, G. Morigi, K. P. Schmidt