Lea Ajzenberger
Numerical Investigation of Quantum Kagome Ice
Experimental measurements of the specific heat of common water ice have revealed a finite entropy at low temperatures ("<“15 K). This phenomenon is attributed to the extensive degeneracy of the ground-state manifold, imposed by the local, divergence-free constraint known as the ice rule. The concept of ice rule was subsequently generalized to other systems, and the classical six-vertex model — describing the six allowed local configurations consistent with the ice rules — has been the subject of extensive study since the 1960s.
The discovery of spin-ice materials renewed interest in the six-vertex model, as the local spin orientations in these systems also obey the ice rule. More recently, research has turned to quantum spin-ice materials with effective spin-1/2 degrees of freedom, where quantum fluctuations may give rise to exotic phases of matter and lift the extensive ground-state degeneracy. In parallel, quantum simulators based on coupled qubits have been used to realize the quantum six-vertex model [1], thereby opening up new directions for exploring two-dimensional quantum ice systems.
The present work extends the quantum six-vertex model to the non-bipartite kagome lattice, employing numerical methods previously applied in the literature [2]. I demonstrate that the notion of topological flux remains well-defined on the kagome lattice. Using exact diagonalization to analyze low-energy excitations, I construct the zero-temperature phase diagram as a function of the relevant tunneling rates. The inclusion of diagonal terms in the Hamiltonian suppresses the first-order phase transition and gives rise to a multicritical point. Finally, I discuss a possible extension of the Rokhsar–Kivelson model to the kagome lattice, which enables an analytical treatment.
[1] A. D. King, C. Nisoli, E. D. Dahl, G. Poulin-Lamarre, and A. Lopez-Bezanilla, Qubit spin ice, Nature 573, 507 (2019).
[2] M. Kondákor and K. Penc, Crystalline phases and devil’s staircase in qubit spin ice, Phys. Rev. Research 5, 043172 (2023).
Mátyás Török
Spontaneous Symmetry Breaking as a Route to Altermagnetism
Altermagnets, a recently identified class of collinear antiferromagnets, exhibit spin-split electronic bands without requiring spin–orbit coupling, provided certain symmetry conditions are met. As antiferromagnetic materials, altermagnets display no net magnetization, which makes them promising candidates for spintronic applications. While altermagnetism originating from explicit crystal-symmetry breaking has been extensively studied using group-theoretical methods and density-functional theory calculations, the role of spontaneous symmetry breaking remains less explored.
In this work, I investigate the emergence of altermagnetism from spontaneous symmetry breaking. My starting point is the model proposed by Leeb et al. [Phys. Rev. Lett. 132, 236701 (2024)], which describes a minimal two-dimensional square lattice with two inequivalent d-orbitals per site. The model incorporates nearest- and next-nearest-neighbor hopping, together with interactions enforcing staggered orbital order and antiferromagnetic order. A mean-field analysis demonstrates how these interactions stabilize an altermagnetic phase.
I first reproduce their findings to establish the underlying mechanism and then extend the framework by introducing spin–orbital octupoles as alternative order parameters. This formalism reveals how octupolar ordering naturally encodes the symmetry patterns required for stable altermagnetism. Finally, I examine the role of on-site electron interactions and coupling to lattice deformations, showing how these additional effects can further stabilize the altermagnetic state.