Olivier Gauthé (École Polytechnique Fédérale de Lausanne)
Tensor network methods for frustrated magnets at finite temperature
Within strongly correlated systems, frustrated magnetism is the field that study magnetic insulators when different microscopic magnetic interactions favor incompatible orders and no classical spin configuration can fulfill all of them. This realm offers a fertile ground for experimental and fundamental exploration, giving rise to unconventional phenomena such as order by disorder or the enigmatic quantum spin liquid phase. Nevertheless, its study poses challenges due to the presence of competing interactions of comparable magnitude, confounding perturbation theory. On the numerical side, frustration usually prevents the use of quantum Monte Carlo algorithms.
Over the last decades, tensor network methods have emerged as the one of the most powerful numerical approach to tackle the many-body problem in both classical and quantum physics. In this talk, we will review the core principles of tensor network and their applications in condensed matter physics. We will focus on strongly correlated systems in two dimensions and discuss the simulation of frustrated quantum magnets at thermal equilibrium using Projected Entangled Pair States (PEPS).
To illustrate this approach, we will address the spin-1/2 Heisenberg model on the square lattice with nearest-neighbor coupling J1 and next-nearest coupling J2 (J1-J2 model) at finite temperature . We will consider both antiferromagnetic (J1 > 0) and ferromagnetic (J1 < 0) cases. We will expose the first unambiguous and direct evidence of an Ising transition associated with the spontaneous breaking of the C_4v symmetry within the collinear antiferromagnet region of the phase diagram.
 O. Gauthé & F. Mila, PRL, 128, 227202 (2022).