Revealing the phase diagram of Kitaev materials by machine learning: Cooperation and competition between spin liquids

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

“…6, the Kitaev contributions to the energy come with sign The three η a,b,c cannot be fixed simultaneously without violating one of the η-constraints, which shows that perturbing the ΓSL with Kitaev interactions is identical to the triangular Ising antiferromagnet with interactions between next nearest neighbour η-variables [3,59,60]. It also presents a clear demonstration of the competition present between Kitaev and Γ interactions of opposite signs [44].…”

“…The classical KΓ model in a small phase space near the pure Kitaev [34][35][36][37][38][39] or pure Γ region was also studied [19,30,[40][41][42][43]. They revealed the macroscopic degeneracy at the pure Kitaev and Γ limits, and the large unit cells (LUCs) that cannot be captured by small clusters used in, for example, ED on the 24-site cluster [44,45].…”

“…Using classical Monte Carlo simulation, we found various LUCs with intriguing four or eight-fold degeneracy except for a few special points with macroscopic degeneracy. It is likely that LUCs are results of the competition between the two frustrated Kitaev and Γ limits [38,44]. Near the Γ dominant region, the bond strength anisotropy further enhances the quantum fluctuations leading to a complete destruction of the magnetic moment suggesting possible QSLs in this region.…”

Hessian-based toolbox for reliable and interpretable machine learning in physics

“…Recently, an alternative route has been explored: machine learning (ML) algorithms can locate phase transitions, even in systems with highly non-trivial order parameters [1,2]. Since then, deep fully connected and convolutional neural networks (CNNs) have been applied to detect phase transitions in a variety of physical models, for classical [1,[3][4][5][6], quantum [2,[7][8][9][10][11][12][13][14][15][16], and topological [17][18][19][20][21] phase transitions with supervised [1,3,5,[13][14][15][16][17][18] and unsupervised [2,4,[6][7][8][9][10][11][12][19][20][21] approaches as well as for experimental data [22][23][24]. Other examples include ML models that do not leverage deep architectures…”

“…In science, the lack of interpretability can be disturbing because the black-box behavior of the models prevents us from learning anything about novel physics. Physicists are already addressing the need for interpretation of ML models, but the majority of proposed methods is either restricted to linear and kernel models [5,6,25,[32][33][34][35][36] or to the particular model architecture [12,32,37] or requires pre-engineering of the data, which limits the results nonuniversally to a specific ML and physical model [21,38]. An interesting, largely model-agnostic method in the context of lattice quantum field theory was proposed in [16].…”