Non-ergodic one-magnon magnetization dynamics of the kagome lattice antiferromagnet

TL;DR

The paper addresses whether closed quantum systems thermalize in the presence of flat bands by studying non-ergodic one-magnon dynamics on the kagomé lattice antiferromagnet. It demonstrates that flat-band localization, via localized magnons, prevents full equilibration and remains in the thermodynamic limit, and develops a decomposition framework using a $J_1$-$J_2$ variant with an enlarged unit cell to interpret the dynamics. The authors provide both analytical basis-construction arguments and large-scale numerical simulations, revealing stationary (localized) and dispersive (delocalized) components and detailing how these behave across parameter choices and system sizes. The results imply robust, disorder-free non-ergodic dynamics in flat-band systems and suggest broad applicability to other frustrated lattices and Hubbard models with flat bands, beyond the $s=1/2$ kagomé case.

Abstract

The present view of modern physics on non-equilibrium dynamics is that generic systems equilibrate or thermalize under rather general conditions, even closed systems under unitary time evolution. The investigation of exceptions thus not only appears attractive, in view of quantum computing where thermalization is a threat it also seems to be necessary. Here, we present aspects of the one-magnon dynamics on the kagome lattice antiferromagnet as an example of a non-equilibrating dynamics due to flat bands. Similar to the one-dimensional delta chain localized eigenstates also called localized magnons lead to disorder-free localization and prevent the system from equilibration.

Figures (15)

• Figure 1: Schematic representation of the kagomé lattice as a $J_1$-$J_2$ model. Dark blue lines denote $J_1$ couplings, light orange both solid and dashed denote $J_2$ couplings. The black dots show the positions of the individual spins, the connections between the dots show the corresponding couplings. Solid: coupling between spins of the same unit cell; dashed: coupling between spins of different unit cells, while the couplings of the periodic boundary conditions are omitted for clarity. The unit cells are numbered in the format $(\nu_1,\nu_2)$. The numbering $i=0,\dots,8$ of the spins within a unit cell is shown using the unit cell $(1,1)$ as an example.
• Figure 2: Left: Schematic representation of a localized magnon in a unit cell of the kagomé lattice with $u=9$ spin per unit cell. The red dots symbolize the spin sites involved in the state. The values next to the dots indicate the non-normalized weight and its sign, i.e. the localized magnon is a superposition of one-magnon excitations from the magnon vacuum at the sites marked in red. Right: For the central unit cell, the hexagon belonging to the stable localized magnon is marked with a blue dot, while the two hexagons of the unstable localized magnons are marked with an orange dot.
• Figure 3: The bands $E^*_\tau$ of the kagomé lattice with $u=9$ and $\alpha=1$ as a function of the reciprocal vector $\vec{q}\in$1.BZ. The boundaries of the first Brillouin zone can be seen as a dotted hexagon. In the diagram for $\tau=4$, the symmetry points $\Gamma, M$ and $K$ (red dots) and the path between them (black, solid) are also shown, cf. Fig. \ref{['fig-kago-band-0-1']}. The energy $E^*_\tau$ is the excitation energy above the flat band.
• Figure 4: The bands $E^*_\tau$ of the kagomé lattice with $u=9$ and $\alpha=1$ as a function of the reciprocal vectors $\vec{q}\in$1.BZ, which lie on the path between the symmetry points $\Gamma, M$ and $K$, cf. Fig. \ref{['fig-kago-band-0']}. The energy $E^*_\tau$ is the excitation energy above the flat band.
• Figure 5: The bands $E^*_\tau$ of the kagomé lattice with $u=9$ for different values of $\alpha$ as a function of the reciprocal vectors $\vec{q}\in$1.BZ, which lie on the path between the symmetry points $\Gamma, M$ and $K$, cf. Fig. \ref{['fig-kago-band-0']}. The energy $E^*_\tau$ is the excitation energy above the flat band.