Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons

Abstract

Spinons are elementary excitations at the core of frustrated quantum magnets. Although it is well-established that a pair of spinons can emerge from a magnon via deconfinement, controlled manipulation of individual spinons and direct observation of their deconfinement remain elusive. We propose an artificial gauge field scenario that enables the engineering of specific excited states in quantum spin models. This generates spatially localized individual spinons with high controllability. By applying time-dependent gauge fields, we realize adiabatic braiding of these spinons, as well as their dynamical evolution in a controllable manner. These results not only provide the first direct visualization of individual spinons localized in the bulk, but also point to new possibilities to simulate their confinement process. Finally, we demonstrate the feasibility of our scenario in Rydberg atoms, which suggests an experimentally viable direction--gauge field engineering of correlated phenomena in excited states.

Figures (4)

• Figure 1: (a) and (b) illustrate the deconfinement of spinons in quantum spin liquids driven by magnetic frustration. (c) (d) schematically indicate the gauge field scenario to engineer excited states in quantum spin models. The gauge field induces higher order topology and localized spinons (marked by red) with high controllability.
• Figure 2: (a) The color plot of $S(q_y,\omega)$ obtained by TDVP on a cylinder geometry where the PBC and OBC are adopted along $y$ and $x$-direction, respectively. The system size, $N_x=24$, $N_y=16$, is used. The dashed circle highlights signatures of in-gap states. (b) The magnon dispersion obtained by spin-wave theory, which is also plot by the dashed white curves in (a) for comparison. (c) shows the edge correlation function $C_{\mathrm{edge}}(j,t)$. The left and right propagation of the spin excitations are highlighted by blue and red lines, respectively. (d) indicates the different velocities between the left and right movers, implying chiral nature of the edge state. This is however absent for quantum spin models supporting topologically trivial magnons (e). $K=1.5$, $D=0.2$, $J=1$ are used for (a)-(d).
• Figure 3: (a) The $Z_2$ lattice gauge field constitute a flux line defined on the quantum spin model. (b) Spin-wave results of the eigenenergies for Eq.\ref{['eqm1']} with a static $Z_2$ gauge field. The red circle denotes degenerate in-gap topological modes. (c) The same as (b) but with further turning magnetic fields, $B=-0.5$, on the sites around the flux line. The inset shows the spatial distribution of the in-gap topological modes. (d) Schematic plot of the edge-reconnection picture accounting for the occurrence of edge modes. (e) shows the wave-function distribution of $|ES_5\rangle$ obtained by DMRG. The distribution for the $|ES_6\rangle$ state is the same. For demonstration, the length of flux line is set to $L=4$ in (b),(c),(e). (f) shows the total $\langle S^z\rangle$ around the left and right ends of the flux line for different system sizes. $K=2$, $D=0.2$, $J=1$ are used for all figures. The system size is 16$\times$12 in (b)(c)(e)
• Figure 4: (a) indicates the dynamic control of the AGF which induces the braiding of the two localized states. (b) The calculated statistical angle $\theta$ for different loops of radius $d$. (c) indicates the alternating gauge field applied on the torus, which generates two different effective mass terms sharing the same domain walls shown in (d). (e)-(h) show the evolution $\langle S^z_{i}\rangle(t)$ starting from the initial state $|ES_5\rangle$, obtained by time-dependent DMRG. $t=0,4,8,24$ for (e),(f),(g),(h), respectively. $T=0.2$ and all other parameters are the same with Fig.\ref{['fig3']}.