Quantums=12antiferromagnets on Archimedean lattices: The route from semiclassical magnetic order to nonmagnetic quantum states

Abstract

We investigate ground states of s=1/2 Heisenberg antiferromagnets on the eleven twodimensional (2D) Archimedian lattices by using the coupled cluster method. Magnetic interactions and quantum fluctuations play against each other subtly in 2D quantum magnets and the magnetic ordering is thus sensitive to the features of lattice topology. Archimedean lattices are those lattices that have 2D arrangements of regular polygons and they often build the underlying magnetic lattices of insulating quasi-two-dimensional quantum magnetic materials. Hence they allow a systematic study of the relationship between lattice topology and magnetic ordering. We find that the Archimedian lattices fall into three groups: those with semiclassical magnetic groundstate long-range order, those with a magnetically disordered (cooperative quantum paramagnetic) ground state, and those with a fragile magnetic order. The most relevant parameters affecting the magnetic ordering are the coordination number and the degree of frustration present.

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

“…Firstly, the method has now been used in well over 100 different papers for a wide variety of frustrated quantum magnets (and see, e.g., Refs. [15,41,[54][55][56] and references cited therein), where the same extrapolation schemes as used here have been utilized, and in virtually all of which the results obtained have been shown to be either the best, or among the best, available. Secondly, in all of the many cases in the literature cited, where it has been possible to compare results obtained from different LSUBn input sets, it has been shown that the obtained extrapolants for all physical parameters agree with one another, typically to ∼ 1% or better.…”

“…For both the GS and ES calculations we employ the well-known lattice animalbased subsystem (LSUBn) truncation hierarchy, which has been much studied and utilized for a wide variety of spin-lattice problems in the past (and see e.g., Refs. [15,41,54,56,68,69,93] and references cited therein).…”

“…The latter plays a large part in ensuring that the method yields accurate, self-consistent, and robust results for a variety of physical parameters for a given system. The method has been applied very widely, yielding results of great (and often unsurpassed) accuracy to systems as diverse as finite nuclei [58], the electron gas (or jellium) [59,60], atoms and molecules of interest in quantum chemistry [64], and a broad spectrum of spin-lattice problems of interest in quantum magnetism [15,41,.…”

“…In the opposite limit, when J ′ → 0, the model reduces to the pure spin-1 2 HAFM (i.e., with NN interactions only) on the square lattice, which has Néel AFM magnetic LRO. In between, when J ′ = J, the model reduces to the pure spin- 1 2 HAFM on another of the 11 2D Archimedean lattices, the GS phase of which is also known to have Néel order [15], which implies (J ′ /J) c > 1. Various theoretical studies (see, e.g., Refs.…”

Frustrated spin systems, an MPS approach

“…This happened partly due to the rise of the geometrically-frustrated AFMs on non-bipartite Archimedean lattices [Diep, 2004, Farnell et al, 2014, Lacroix et al, 2011, Lhuillier, 2005, Lhuillier and Misguich, 2001, Sachdev, 2011, Schollwöck et al, 2004 (geometrical frustration is a type of frustration where the competition between Hamiltonian terms comes from the arrangement of spins on non-trivial lattice plaquettes -see below). Interestingly, the existence of geometrical frustration is enough by itself to often lead to the 'melting' of the magnetic ordering, stabilizing a family of nonmagnetic phases, collectively classified as spin liquids (also known as paramagnetic states [Balents, 2010, Chen et al, 2010, Kalmeyer and Laughlin, 1987, Read and Sachdev, 1991, Wen, 1991, Wen et al, 1989, Wen, 2002; spin glasses [Diep, 2004, Lacroix et al, 2011, Sachdev, 2011 form the other type of quantum states with vanishing average magnetization that are essentially stabilized due to the frustration, however, are not considered in this thesis).…”