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arXiv:cond-mat/0406103 · Physical Review B

Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice

Johannes Richter, J. Schulenburg, A. Honecker, D. Schmalfuß

Published Nov 29, 2004• 77 citations
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Abstract

We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization, and a variational mean-field approach. We find evidence that the star lattice is (besides the kagom\'e lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star lattice exhibits a huge nontrivial degeneracy like on the kagom\'e lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.

DOI
10.1103/physrevb.70.174454

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We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1

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We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization, and a variational mean-field approach. We find evidence that the star lattice is (besides the kagom'e lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star lattice exhibits a huge nontrivial degeneracy like on the kagom'e lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.
We investigate various competing paramagnetic ground states of the Heisenberg antiferromagnet on the two-dimensional star lattice which exhibits geometric frustration. Using slave particle mean-field theory combined with a projective symmetry group analysis, we examine a variety of candidate spin liquid states on this lattice, including chiral spin liquids, spin liquids with Fermi surfaces of spinons, and nematic spin liquids which break lattice rotational symmetry. Motivated by connection to large-NNN SU(N)\text{SU}(N)SU(N) theory as well as numerical exact diagonalization studies, we also examine various valence-bond solid (VBS) states on this lattice. Based on a study of energetics using Gutzwiller projected states, we find that a fully gapped spin liquid state is the lowest-energy spin liquid candidate for this model. We also find from a study of energetics using Gutzwiller projected wave functions and bond operator approaches that this spin liquid is unstable toward two different VBS states---a VBS state which respects all the Hamiltonian symmetries and a VBS state which exhibits $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ order---depending on the ratio of the Heisenberg exchange couplings on the two inequivalent bonds of the lattice. We compute the triplon dispersion in both VBS states within the bond operator approach and discuss possible implications of our work for future experiments on candidate materials.
Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.
We study the ground state properties of a quantum antiferromagnet on the kagom\'e lattice in the presence of a magnetic field, paying particular attention to the stability of the plateau at magnetization 1∕31∕31∕3 of saturation and the nature of its ground state. We discuss fluctuations around classical ground states and argue that quantum and classical calculations at the harmonic level do not lead to the same result in contrast to the zero-field case. For spin S=1∕2S=1∕2S=1∕2 we find a magnetic gap below which an exponential number of nonmagnetic excitations are present. Moreover, such non-magnetic excitations also have a (much smaller) gap above the threefold degenerate ground state. We provide evidence that the ground state has long-range order of valence-bond crystal type with nine spins in the unit cell.
We investigate the spin-1 kagome-lattice Heisenberg antiferromagnet using large-scale Lanczos diagonalization and the finite-temperature Lanczos method. The zero-temperature magnetization process exhibits plateaus at m = 0 , 1 / 3 , 7 / 9 , and 8 / 9 , where m is the normalized magnetization. The m = 0 plateau is identified as a trimer valence-bond-crystal state, while the high-field plateaus at m = 7 / 9 and 8 / 9 are identified as magnon crystals. In particular, the m = 8 / 9 plateau corresponds to the exact localized-magnon crystal state. A smoothed zero-temperature magnetization curve constructed using the Gaussian-kernel smoothing method indicates magnetization jumps at the lower-field edge of the m = 1 / 3 plateau and at the upper-field edges of the m = 7 / 9 and 8 / 9 plateaus. At finite temperatures, the specific heat exhibits a double-peak structure with peaks around T / J ≃ 0.1 and T / J ≃ 1.1 , and the low-temperature peak may be related to trimer valence-bond-crystal ordering. The finite-temperature magnetization curves show that the m = 1 / 3 plateau remains visible at low temperatures, whereas the high-field plateaus are rapidly smeared out by thermal effects. These results provide benchmark data for thermodynamic and high-field magnetization measurements in candidate spin-1 kagome-lattice materials.
This paper is concerned with physics of the low-energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse-field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases---an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.
We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1