Exact quantum scars of frustrated hardcore bosons for cross-platform realizations

Abstract

Quantum many-body scars are nonthermal states exhibiting persistent revivals in an otherwise ergodic, nonintegrable quantum system. Existing examples of exact quantum scars, however, have not yet been amenable to direct experimental demonstration. Here we show that a minimal model of hardcore bosons hopping on a $π$-flux ladder is sufficient to give rise to an exact scar due to kinetic frustration. The simplicity of this model makes it suitable for multiple existing quantum simulation platforms, which we illustrate with proposals for cold atom Bose-Hubbard simulators and polar molecule or Rydberg atom tweezer arrays. In these platforms, the scar lifetime can be extended by tuning experimentally accessible parameters, like the Hubbard interaction or a Floquet drive. Finally, we introduce a practical heuristic based on the energy distribution of eigenstates for systematically predicting and optimizing quantum many-body scar lifetimes. Their cross-platform realizability and long lifetimes make them well-suited for benchmarking coherence and exploring nonergodic dynamics in current and near-term quantum devices.

Figures (11)

• Figure 1: Exact quantum many-body scars in a hardcore boson ladder with $\pi$-flux per plaquette. (a) Illustration of a $L = 5$ ladder with hardcore bosons tunneling as $-t_\parallel$ in the top leg, $t_\parallel$ in the bottom leg, and $t_\perp$ on the rungs. Our QMBS state is pictured as a filled bottom leg (black circles) and an unoccupied top leg. The destructive interference from tunneling around one square plaquette leads to a $\pi$-flux. (b) In one plaquette, destructive interference of the initial state (left) evolving into a final, non-scar configuration (right) is illustrated, via two potential paths (top and bottom) whose amplitudes carry a relative $\pi$ phase shift. (c) The nearest-neighbor energy level spacing distribution of the model defined in Eq. \ref{['eq:exactscar']} for a $L=9$ ladder with a small second-nearest neighbor hopping that preserves the scar (see End Matter for details). The spacings follow a Wigner-Dyson distribution (blue curve), indicating non-integrability of the model. (d) Dynamics of the scar, showing the time-evolution of the many-body fidelity $F(t)$ (left axis, blue line) and the observable $\langle n^{\textrm{imb}}\rangle$ (right axis, red line) for a $L = 10$ ladder with $t_\perp = t_\parallel$. (e) The entanglement entropy $S_A$ of the ladder split across the middle as a function of energy for $L=8$ ladder, calculated at half-filling. The scar states are in red.
• Figure 2: Implementation of the model using ultracold bosonic atoms experiencing an artificial magnetic field. (a) The approximate QMBS comprises a half-filled boson ladder (black circles). The lattice setup includes a uniform sinusoidal potential in $x$ and a staggered double-well in $y$, with energy offset $\Delta$ and lattice constant $d$. A pair of Raman lasers (blue arrows) with wavevectors $\mathbf{k_1,k_2}$ induce photon-assisted tunneling in $y$ via an optical two-photon transition using the atom's excited state $|g\rangle\rightarrow|e\rangle$. Nearest neighbor complex- and real-valued tunnelings with magnitudes $J',J$, respectively, couple the $y$ and $x$ directions. With appropriate choice of Raman laser detunings and angles, each plaquette has an effective $\pi$-flux. (b) Dynamics of the scar for $L$ = 7, showing $\langle n^{\textrm{imb}} \rangle$ for various $U/|J|=U/|J'|$. For infinite interactions, the bosons obey a hardcore constraint, leading to persistent revivals.
• Figure 3: Implementation of the model using dipolar spin-1/2 degrees of freedom. (a) Transformation of the two-leg hardcore boson ladder of Fig. \ref{['fig:1']}a into a dipolar zig-zag chain. Rydberg atoms or polar molecules trapped in optical tweezers form a spin-1/2 system spanned by two internal states ($\ket{\downarrow}, \ket{\uparrow}$), and they interact under the spin-exchange Hamiltonian $\hat{H}_{SE}$. (b) Relevant parameters of the dipolar zig-zag chain with six sites pictured. Intra-rung interactions (in red) $J_{01}$ couple $n,n+1$ with $n$ even. Next-nearest-neighbor couplings (in solid grey) are zero at the magic angle of $1-3\cos^2\theta=0$. Blue and orange lines indicate $J_{02}$ and $J_{13}$, with angles of $\alpha$ and $\beta$ with respect to the zig-zag chain, respectively. Longer-range couplings are indicated in dashed grey lines. (c) Dynamics of the dipolar QMBS showing $\langle n^{\rm imb}\rangle$ (in blue). The scar lifetime can be extended by Floquet-engineering (in purple) to cancel the longer-range couplings, with the Floquet pulse sequence given in the inset (see text for details). The long-lived scar exists in contrast to typical thermal states (in grey), which show fast decay of oscillations (see End Matter for numerical details).
• Figure 4: Predicting the thermalization time of an approximate QMBS from its energy distribution. Due to experimental limitations, the approximate QMBS states exhibit finite lifetimes $\tau$ in both the $\pi$-flux boson ladder taking $|J'|=|J|$ (a) and the dipolar spin chain (b), where each point is a different parameter -- varying the Hubbard $U$ or the angles for the dipolar zig-zag chain, respectively [see Supplement for details]. The top left insets show the eigenenergy distribution for one such Hamiltonian, revealing a spread compared to an exact scar's equally spaced tower of eigenstates (grey lines). From this, we extract the fractional energy distribution (bottom right insets), fitting the width $2\sigma$ given by the grey shaded area. Here $P$ is the weighted probability distribution of the overlap between QMBS state and many-body eigenstates. There is a clear linear relationship between $\tau$ and $1/\sigma$ for both models, allowing us to optimize the scar lifetime using the energy distributions.
• Figure S1: Nearest neighbor spacing ratio with $t_{nnn}$ and $L$.(a)$\langle r \rangle$ value in $S_z = 0, K_x = 0, P_y = 1, P_x' = 1, F = 1$ sector. $t_{nnn}$ is the next-next nearest neighbor hopping strength. The purple and green dashed lines indicate $\langle r\rangle$ for Wigner-Dyson and Poissonian distributions, respectively. (b)$\langle r \rangle$ value in $N_{\textrm{up}} = 6, K_x = 0, P_y = 1, P_x' = 1$ sector for different system size for $t_{nnn}=0$. The inset shows the level spacing distribution for $L = 18$. Blue and dashed blue curve in the inset correspond to Wigner-Dyson and Poisson distributions, respectively.