A Tensor Network Study of Cubic Anisotropy.

Title: A Tensor Network Study of Cubic Anisotropy.
Speaker: Naoki Kawashima (ISSP/U. Tokyo)
Start Date/Time: 2022-05-31 / 12:30 (Taipei time)
End Date/Time: 2022-05-31 / 14:00
Venue: Online Zoom [Registration] is required
Host : Prof. Ying-Jer Kao (Department of Physics, NTU)

Abstract: Though the cubic anisotropy is quite common in nature, spin systems with this anisotropy do not seem to have been studied so intensively, compared to countless publications on its isotropic counterpart. One of the reasons for this may be that we usually do not expect anything fancier about this system than the old problem concerning the lower-critical dimension for the cubic fixed point [1]. Another reason, though not so widely appreciated, may be the technical difficulty; there has been no algorithm that works. It is relatively easy to construct an algorithm for quantum Monte Carlo simulation with no negative signs, following the general prescription of local/loop/cluster updates, that can work in principle for the Heisenberg model with cubic spin anisotropy. However, as soon as we start simulation, we get stuck. To my knowledge, there is no QMC algorithm that works in practice. Recently, we carried out tensor network calculation of the model, and established the phase diagram for the S=2 model [2]. The phase diagram we obtained qualitatively agree with the mean-field analysis by Dom{{body}}#39;anski and Sznajd [3]. We also found a peculiar non-interacting quantum transition point where two cubic transition lines intersect. While the point itself is trivial (a product state), the system exhibits emergent U(1) symmetry in its vicinity, and the correlation length diverges towards this point. 

[1] For example, H. Kleinert, S. Thoms and V. Schulte-Frohlinde, Phys.
Rev. B 56 14428 (1997), and J. M. Carmona, A. Pelissetto and E. Vicari,
Phys. Rev. B 61 (15136).
[2] W.-L. Tu, S. R. Ghazanfari, H.-K. Wu, H.-Y. Lee and N. Kawashima:
[3] Z. Dom{{body}}#39;anski and J. Sznajd, J. of Magn. Magn. Mat. 71, 306 (1988).
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