Quantum phase transitions for the Haldane system in higher dimensions: A mixed-spin cluster expansion approach

昌久 古賀, Akihisa Koga

Akihisa Koga, Norio Kawakami

We present a mixed-spin cluster expansion method to discuss the quantum phase transitions for the Haldane system in two and three dimensions. By mapping the $s=1$ antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer, and the magnetically ordered phases. The mixed-spin cluster expansion proposed here realizes the notion of the valence bond solid in a perturbation theory. This method allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The zero-temperature phase diagram is thus determined rather precisely for the two- and three-dimensional Haldane systems.

Akihisa Koga, Norio Kawakami

We present a novel mixed-spin cluster expansion method for a quasi-one-dimensional Haldane system with bond alternation. By mapping the s=1 antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer and the magnetically ordered phases. The mixed-spin cluster expansion proposed here allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The phase diagram is determined rather precisely by making use of an additional symmetry property in the effective mixed-spin model introduced.

Hiroshi Miyazaki, Tomohiko Hiwasa, Masataka Oko +1 more

Jean‐Philippe Boucher

Patrick Adelhardt, Julian Gritsch, M. Hille +2 more

We use linked-cluster expansions to analyze the quantum phase transitions between symmetry-unbroken trivial and topological Haldane phases in two different spin-one chains. The first model is the spin-one Heisenberg chain in the presence of a single-ion anisotropy, while the second one is the dimerized spin-one Heisenberg chain. For both models, we determine the ground-state energy and the one-particle gap inside the nontopological phase as a high-order series using perturbative continuous unitary transformations. Extrapolations of the gap series are applied to locate the quantum critical point and to extract the associated critical exponent. We find that this approach works unsatisfactorily for the anisotropic chain, since the quality of the extrapolation appears insufficient due to the large correlation length exponent. In contrast, extrapolation schemes display very good convergence for the gap closing in the case of the dimerized spin-one Heisenberg chain.