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arXiv:cond-mat/0110283 · Recent Progress in Many-Body Theories

QUANTUM PHASES IN TWO-DIMENSIONAL FRUSTRATED SPIN-1/2 ANTIFERROMAGNETS

Philippe Sindzingre, C. Lhuillier, J.-B. Fouet

Published Dec 1, 2002• 3 citations
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Abstract

We describe four phases found in two-dimensional quantum antiferromagnets. Two of them display long range order at T=0: the Néel state and the Valence Bond Crystal. The last two are Spin-Liquids. Properties of these different states are shortly described and likely conditions of their occurence outlined.
DOI
10.1142/9789812777843_0011

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The large-N limit of a nearest-neighbor SU(N) antiferromagnet on a bipartite lattice exhibits in dimensions d\ensuremath{\ge}2 a zero-temperature phase transition between a N\'eel ordered state and a resonating-valence-bond state. Here it is shown in d=1,2 that topological effects produce spin-Peierls or valence-bond-solid order in the non-N\'eel phase with a ground-state degeneracy which varies periodically with ``spin'' for fixed N with periodicity given by the coordination number of the lattice. Thus a non-N\'eel phase of the spin-(1/2 Heisenberg model on a square lattice would be a spin-Peierls state with a fourfold degeneracy due to broken lattice rotational symmetry.

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We study the T=0T=0T=0 phase diagrams of models of bilayers of S=1/2S=1/2S=1/2 square lattices antiferromagnets with SU(2) Heisenberg symmetry that have 2, 4, and 6 spin exchanges. We study two families of bilayer models with distinct internal symmetries and, hence, different phase diagram topologies. A traditional bilayer model in which the interlayer interaction is Heisenberg so that the two layers can exchange spin (and energy) with each other, making it possible to achieve a simple dimerized valence bond liquid-like state. The resulting phase diagram is rich with Néel, valence bond solid and simple dimer phases, and both first-order and continuous transitions, which we demonstrate are consistent with the conventional Landau theory of order parameters. In the second family of models in which the layers can exchange only energy but no spin (reminiscent of the Ashkin-Teller coupling), the simple dimer state cannot occur. The phase diagrams reveal a number of phase transitions that are accessed for the first time. We find that the phase transition between Néel and VBS is first order in both the spin-spin and energy-energy coupled models, although they have strikingly distinct finite-size scaling behavior and that the transition from VBS to dimer in the spin-spin coupling model deviates from the expected scenario of an XY model with dangerously irrelevant four-fold anisotropy.
We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5<J(2)/J(1)<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J(2)/J(1)<0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.
The large-N limit of a nearest-neighbor SU(N) antiferromagnet on a bipartite lattice exhibits in dimensions d\ensuremath{\ge}2 a zero-temperature phase transition between a N\'eel ordered state and a resonating-valence-bond state. Here it is shown in d=1,2 that topological effects produce spin-Peierls or valence-bond-solid order in the non-N\'eel phase with a ground-state degeneracy which varies periodically with ``spin'' for fixed N with periodicity given by the coordination number of the lattice. Thus a non-N\'eel phase of the spin-(1/2 Heisenberg model on a square lattice would be a spin-Peierls state with a fourfold degeneracy due to broken lattice rotational symmetry.