Emergent chiral Higgs mode in $π$-flux frustrated lattices

Abstract

Neutral-atom quantum simulators provide a powerful platform for realizing strongly correlated phases, enabling access to dynamical signatures of quasiparticles and symmetry breaking processes. Motivated by recent observations of quantum phases in flux-frustrated ladders with non-vanishing ground state currents, we investigate interacting bosons on the dimerized BBH lattice in two dimensions-originally introduced in the context of higher-order topology. After mapping out the phase diagram, which includes vortex superfluid (V-SF), vortex Mott insulator (V-MI), and featureless Mott insulator (MI) phases, we focus on the integer filling case. There, the MI/V-SF transition simultaneously breaks the $\mathbb Z_2^{T}$ and U(1) symmetries, where $\mathbb Z_2^{T}$ corresponds to time-reversal symmetry (TRS). Using a slave-boson description, we resolve the excitation spectrum across the transition and uncover a chiral Higgs mode whose mass softens at criticality, providing a dynamical hallmark of emergent chirality that we numerically probe via quench dynamics. Our results establish an experimentally realistic setting for probing unconventional TRS-broken phases and quasiparticles with intrinsic chirality in strongly interacting quantum matter.

Figures (8)

• Figure 1: Model and main results. (a) Schematics of the BBH lattice with dimerized hopping $J$, $J'$ and uniform $\pi$ flux for interacting bosons. The unit cell is highlighted. (b) Ground-state loop current $\langle \hat{\mathcal{L}}\rangle$ (black circles) and superfluid order parameter $|\psi|$ (red triangles) within cluster Gutzwiller approximation marking phase transitions between vortex superfluid (V-SF) and vortex Mott insulating (V-MI) phases for filling $\nu = 1/4$ (top) and between V-SF and Mott-insulating (MI) phases for $\nu = 1$ (bottom) for $J'/J=0.03$. The region displaying a chiral Higgs excitation is highlighted. (c) Pictorial representation of chiral Higgs mode dynamics within a plaquette, where $\delta \psi_{i}$ indicates the amplitude excitation and the mode exhibits a finite loop current.
• Figure 2: Phase diagram for $J'/J = 0.03$ of the 2D BBH model via cluster Gutzwiller approximation ($n_{\text{max}}=5$). (a) Colormap of the superfluid order parameter $|\psi|$ showing Mott phase (MI), vortex Mott phases (V-MI) at different fillings and the vortex superfluid phase (V-SF). (b) Corresponding loop current per particle across the phase diagram. Notice that only the Mott lobe at $\nu=1$ has zero loop current, while fractional fillings exhibit $\langle \hat{\mathcal{L}} \rangle \neq 0$, indicating a V-MI phase. Inset shows the current pattern in V-SF and V-MI phases.
• Figure 3: DMRG numerical results for a ladder with $J'/J=0.1$. (a) Ladder geometry for DMRG simulations. (b)-(c) Fidelity susceptibilities $\chi_{\mathcal{F}}$ for $\nu=1/4$ and $\nu=1$. The peaks growing with system size are indication of the phase transition. (d)-(e) Loop current per particle $|\langle \hat{\mathcal{L}} \rangle | / \langle \hat{n} \rangle$ for $L_{x}=106$ ($\nu=1/4$) and for $L_{x}=48$ ($\nu=1$). The $\nu=1$ curve and the drop of loop current show the V-SF / MI phase transition. Insets show the $\mathcal{C}_p$ correlator corresponding to the filled symbols.
• Figure 4: Low-energy excitations in the V-SF phase for filling $\nu = 1$. (a)-(c) Quasiparticle excitations for $|\mathbf{k}_x| = |\mathbf{k}_y| = k$, $J'/U = 0.03$, $J/U = 1.0$, and $\mu/U = -0.68$, corresponding to the cross symbols in Fig. \ref{['Fig2']}. Spectra are colored based on the values of (a) flatness $\mathcal{F}_{\alpha, k}$, (b) plaquette density and (c) loop current $\langle \mathcal{\hat{L}} \rangle_{\alpha,k}$. The index $\alpha=1,\dots, 5$ labels the modes for increasing value of energy (d) Loop current per particle, $\langle \hat{\mathcal{L}} \rangle_{\alpha} / \langle \hat{n} \rangle$ for H1 and H2. Filled symbols corresponds to spectra shown in the upper panel. (e) cGWA time evolution of loop current (black line) and local order parameter (red line) normalized to their ground-state values following a quench of a staggered flux $\pm\delta\theta$ per plaquette at unit filling. Parameters as in (a)-(c) and $\delta\theta = 0.01 (J-\bar{J})/\bar{J}$ with $\bar{J}=0.88\,U$. (f) Power spectrum of the loop current time evolution for different values $J/U$. Dashed lines highlight the frequencies corresponding to H1 (red) and H2 (white) modes.
• Figure S1: (a) Phase diagram along the cut at fixed $J/U=1.2$. White dots mark the transition points from the V-SF (right) to the (V-)MI (left), while the dotted curves shows the constant filling lines for $\nu=1$ (red) and $\nu=1/2$ (blue). The vertical axis shows the ground-state loop current. The lobe at integer filling exhibits zero loop current, while the fractional-filling lobes correspond to V-MI phases with finite current. (b) Control parameter at integer (red) and half (blue) filling for $J/U=1.2$ as a function of $J ' /U$. The control parameter displays a peak at the transition point and remains below $\epsilon \sim 0.04$.