Perfect quantum state transfer through a chaotic spin chain via many-body scars

TL;DR

The paper shows that perfect quantum state transfer can be realized in strongly interacting, chaotic spin chains by leveraging a sparse set of quantum many-body scar (QMBS) states embedded within the thermal spectrum. By constructing scarred Hamiltonians with projector-based perturbations, the authors create a dedicated QMBS subspace that supports coherent transport even as the bulk remains chaotic. They demonstrate this in both spin-1/2 and spin-1 chains, with the transfer governed by an SU(2)-structured effective dynamics and protected by non-local symmetries. The work suggests a practical use of QMBS for robust quantum information tasks in non-integrable systems and discusses robustness, minimality of embedding, and connections to projector-embedding frameworks.

Abstract

Quantum many-body scars (QMBS) offer a mechanism for weak ergodicity breaking, enabling non-thermal dynamics to persist in a chaotic many-body system. While most studies of QMBS focus on anomalous eigenstate properties or long-lived revivals of local observables, their potential for quantum information processing remains largely unexplored. In this work, we demonstrate that \emph{perfect quantum state transfer} can be achieved in a strongly interacting, quantum chaotic spin chain by exploiting a sparse set of QMBS eigenstates embedded within an otherwise thermal spectrum. These results show that QMBS in chaotic many-body systems may be harnessed for information transport tasks typically associated with integrable models.

Figures (4)

• Figure 1: (a) The aim of the quantum state transfer protocol is to transmit an arbitrary spin-1/2 state $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$ across the chain. In this paper we focus on state transfer implemented by time-independent Hamiltonian dynamics. (b) Perfect state transfer via $\hat{H}_{\rm PST}$ can be understood intuitively as precession of an effective spin-$(N-1)/2$, embedded in the many-body Hilbert space, which transports a spin excitation across the chain. This effective spin is preserved in our many-body scarred Hamiltonian $\hat{H}_{\rm scar} = \hat{H}_{\rm PST} + \sum_n \hat{P}_n\hat{h}_n \hat{P}_n$, while the remainder of the spectrum is thermalised.
• Figure 2: (a) Time evolution of the transfer fidelity through a spin-1/2 chain, starting from either the initial state $|\Psi(0)\rangle = |\psi\rangle|0\rangle^{\otimes (N-1)}$ (heavy lines) or $|\overline{\Psi}(0)\rangle = |\psi\rangle|1\rangle^{\otimes (N-1)}$ (light lines), where $|\psi\rangle = (|0\rangle+|1\rangle)/\sqrt{2}$. Evolution by the Hamiltonian $\hat{H}_{\rm PST}$ results in perfect state transfer for either initial state, at times $\tau_m = (m-1/2)\pi/\lambda$ where $m\in\{1,2,3,\hdots \}$ (vertical dashed black lines). Adding a generic local interaction $\hat{H}_{\rm thermal} = \hat{H}_{\rm PST} + \sum_n \hat{h}_n$ severely inhibits state transfer for both initial states (red lines). Adding the projected local interaction, $\hat{H}_{\rm scar} = \hat{H}_{\rm PST} + \sum_n \hat{P}_n\hat{h}_n \hat{P}_n$ supports perfect state transfer for the initial state $|\Psi(0)\rangle$ (heavy blue line), due to the QMBS, but not for the initial state $|\overline{\Psi}(0)\rangle$ (light blue line) which is outside the QMBS subspace. (b,c) Level spacing statistics show that both $\hat{H}_{\rm thermal}$ (b) and $\hat{H}_{\rm scar}$ (c) are chaotic. (d,e) The entanglement entropy of the eigenstates of $\hat{H}_{\rm thermal}$ and $\hat{H}_{\rm scar}$ generally follow a volume law scaling. However, $\hat{H}_{\rm scar}$ has a small number of non-thermal eigenstates, which are responsible for the perfect state transfer despite the model being chaotic. [Other parameters: $N=12$, $\omega=0$.]
• Figure 3: (a) Time evolution of the transfer fidelity through a spin-1 chain, starting from either the initial state $|\Psi(0)\rangle = |\psi\rangle|+\rangle^{\otimes (N-1)}$ (heavy lines) or $|\overline{\Psi}(0)\rangle = |\psi\rangle|-\rangle^{\otimes (N-1)}$ (light lines), where $|\psi\rangle = (|+\rangle+|-\rangle)/\sqrt{2}$. Evolution by the Hamiltonian $\hat{H}^{(1)}_{\rm PST}$ results in perfect state transfer for either initial state. Adding generic two-body local interactions (Eq. \ref{['eq:H_thermal_spin1']}) severely inhibits state transfer for both initial states (red lines). However, adding the projected local interaction (Eq. \ref{['eq:H_scar_spin1']}) supports perfect state transfer for the initial state $|\Psi(0)\rangle$ (heavy blue line). (b,c) Level spacing statistics show that both $\hat{H}_{\rm thermal}^{(1)}$ (b) and $\hat{H}_{\rm scar}^{(1)}$ (c) are chaotic. (d,e) The entanglement entropy of the eigenstates of $\hat{H}_{\rm thermal}^{(1)}$ and $\hat{H}_{\rm scar}^{(1)}$ generally follow a volume law scaling. However, $\hat{H}_{\rm scar}^{(1)}$ has a small number of non-thermal eigenstates, which are responsible for the perfect state transfer despite the model being chaotic and strongly interacting. [Other parameters: $N=8$, $\omega=0$, $\hat{h}_{n,n'} = \frac{1}{2}(\hat{A}_{n,n'} + \hat{A}_{n,n'})/|n-n'|^3$ where $\hat{A}_{n,n'}$ is a two-spin operator whose matrix elements are complex Gaussian random variables with zero mean and unit variance.]
• Figure 4: The state transfer infidelity, at time $t = \pi/2\lambda$, in the presence of three different perturbation types: (a) $\hat{H}_{\rm global-X} = \epsilon\sum_n \hat{S}_n^x$, (b) $\hat{H}_{\rm local-X} = \epsilon \hat{S}_{N/2}^x$, (c) $\hat{H}_{\rm global-YY} = \epsilon\sum_n \hat{S}_n^y \hat{S}_{n+1}^y$. Here, $N=8$ and all other initial conditions and parameters in $\hat{H}_{\rm scar}^{(1)}$ are generated in the same way as in Fig. \ref{['fig:state_transfer_spin1']}.