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Journal of Physics C Solid State Physics

Quantum renormalisations in the one-dimensional easy-plane antiferromagnet

Sérgio Luiz Talim, Antonio S. T. Pires

Published Jul 30, 1988• 0 citations
Publisher
DOI
10.1088/0022-3719/21/21/521

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Phase diagram, critical properties and thermodynamic functions of the two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated globally using a numerical renormalisation group theory. The nearest-neighbour spin-spin correlations and entanglement properties, as well as internal energy and specific heat are calculated globally at all temperatures for the whole range of exchange interaction anisotropy, from XY limit to Ising limits, for both antiferromagnetic and ferromagnetic cases. We show that there exists long-range (quasi-long-range) order at low-temperatures, and the low-lying excitations are gapped (gapless) in the Ising-like easy-axis (XY-like easy-plane) regime. Besides, we identify quantum phase transitions at zero-temperature.
Two-dimensional quantum systems with competing orders can feature a deconfined quantum critical point, yielding a continuous phase transition that is incompatible with the Landau-Ginzburg-Wilson scenario, predicting instead a first-order phase transition. This is caused by the LGW order parameter breaking up into new elementary excitations at the critical point. Canonical candidates for deconfined quantum criticality are quantum antiferromagnets with competing magnetic orders, captured by the easy-plane CP^{1} model. A delicate issue however is that numerics indicates the easy-plane CP^{1} antiferromagnet to exhibit a first-order transition. Here we show that an additional topological Chern-Simons term in the action changes this picture completely in several ways. We find that the topological easy-plane antiferromagnet undergoes a second-order transition with quantized critical exponents. Further, a particle-vortex duality naturally maps the partition function of the Chern-Simons easy-plane antiferromagnet into one of massless Dirac fermions.
The dynamics of a one-dimensional Heisenberg antiferromagnet with a small Dzyaloshinski–Moriya component to the exchange interaction is considered. The spin rotational invariance within the easy plane is broken by the application of a weak magnetic field in the easy plane. The nature of the spin-wave excitations of the quantum spin system is investigated, and pronounced anomalies in the single-spin-wave spectrum at fields comparable to the anisotropy in the exchange interaction are found. These anomalies are of quantum character and are related to the resonance between the single-spin-wave and the two-spin-wave excitations. The implications for the two-spin-wave bound states are discussed.