Nonperturbative linked-cluster expansions in long-range ordered quantum systems
Ixert D, Schmidt KP (2016)
Publication Status: Published
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: AMER PHYSICAL SOC
Book Volume: 94
Journal Issue: 19
DOI: 10.1103/PhysRevB.94.195133
Abstract
We introduce a generic scheme to perform nonperturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge fields in the exact diagonalization on clusters, which break the associated symmetry of the ordered phase. Two approaches, based either on a self-consistent solution of the order parameter or on minimal sensitivity with respect to the ground-state energy per site, are formulated to find the optimal edge field in each NLCE order. Furthermore, we investigate the scaling behavior of the NLCE data sequences towards the infinite-order limit. We apply our scheme to gapped and gapless ordered phases of XXZ Heisenberg models on various lattices and for spins 1/2 and 1 using several types of cluster expansions ranging from a full-graph decomposition, rectangular clusters, up to more symmetric square clusters. It is found that the inclusion of edge fields allows to regularize nonperturbative linked-cluster expansions in ordered phases yielding convergent data sequences. This includes the long-range spin-ordered ground state of the spin-1/2 and spin-1 Heisenberg model on the square and triangular lattice as well as the trimerized valence bond crystal of the spin-1 Heisenberg model on the kagome lattice.
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Germany (DE)How to cite
APA:
Ixert, D., & Schmidt, K.P. (2016). Nonperturbative linked-cluster expansions in long-range ordered quantum systems. Physical Review B, 94(19). https://doi.org/10.1103/PhysRevB.94.195133
MLA:
Ixert, Dominik, and Kai Phillip Schmidt. "Nonperturbative linked-cluster expansions in long-range ordered quantum systems." Physical Review B 94.19 (2016).
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