The far-from-equilibrium dynamics of certain interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to long-lived oscillations. Despite the success of viewing scars from the perspectives of symmetry, commutant algebra and quasiparticles, it remains a challenge to elucidate the mechanism underlying all QMBS and to distinguish them from other forms of ergodicity breaking. In this work, we introduce an alternative route to detect and diagnose QMBS based on Fisher zeros, i.e., the patterns of zeros of the analytically continued partition function
Z on the complex
β (inverse temperature) plane. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary
β axis and extend upward, separating the
β-plane into regions with distinctive thermalization behaviors. This conjecture is motivated from interpreting the complex
Z as the return amplitude of the thermofield double state, and it is validated by analyzing two models with QMBS, the
PˉXPˉ model and the Ising chain in external fields. These models also illustrate the key difference between QMBS and strong ergodicity breaking including their distinctive renormalization group flows on the complex
β-plane. This ``statistical mechanics" approach places QMBS within the same framework of thermal and dynamical phase transitions. It has the advantage of spotting scars without exhaustively examining each individual quantum state.
The far-from-equilibrium dynamics of certain interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to long-lived oscillations. Despite the success of viewing scars from the perspectives of symmetry, commutant algebra, and quasiparticles, it remains a challenge to elucidate the mechanism underlying all QMBS and to distinguish them from other forms of ergodicity breaking. In this work, we introduce an alternative route to detect and diagnose QMBS based on Fisher zeros, i.e., the patterns of zeros of the analytically continued partition function Z on the complex β (inverse temperature) plane. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary β axis and extend upward, separating the β plane into regions with distinctive thermalization behaviors. This conjecture is motivated from interpreting the complex Z as the return amplitude of the thermofield double state, and it is validated by analyzing two models with QMBS, the P[over ¯]XP[over ¯] model and the Ising chain in external fields. These models also illustrate the key difference between QMBS and strong ergodicity breaking including their distinctive renormalization group flows on the complex β plane. This "statistical mechanics" approach places QMBS within the same framework of thermal and dynamical phase transitions. It has the advantage of spotting scars without exhaustively examining each individual quantum state.
One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic quantum matter, such as many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS). In addition to conventional QMBS, a recently discovered mechanism for ergodicity violation are the so-called asymptotic quantum many-body scars (AQMBS). These become more stable as system size is increased, leading to progressively longer thermalisation timescales. In this work, we show a connection between gapless excitations and AQMBS in certain qudit-based models. We then consider a 2-local model, hosting both conventional and asymptotic scars, in which the AQMBS states are gapless excitations of a ground state localisation transition. By exploiting the structure of the found AQMBS states and the all-to-all connectivity of the Quantinuum H1-1 quantum processor, we prepare these states in logarithmic circuit depth, and probe their thermalisation behaviour under Floquet dynamics. Performing simulations on up to N = 20 qubits and up to 418 entangling ZZ gates, we find slower thermalisation times as the system size is increased, providing the first experimental signatures of asymptotic scars.
Weak ergodicity breaking, particularly through quantum many-body scars (QMBS), has become a significant focus in many-body physics. Krylov state complexity quantifies the spread of quantum states within the Krylov basis and serves as a powerful diagnostic for analyzing nonergodic dynamics. In this work, we study spin-one XXZ magnets and reveal nonergodic behavior tied to QMBS. For the XY model, the nematic N\'eel state exhibits periodic revivals in Krylov complexity. In the generic XXZ model, we identify spin helix states as weakly ergodicity-breaking states, characterized by low entanglement and nonthermal dynamics. Across different scenarios, the Lanczos coefficients for scarred states display an elliptical pattern, reflecting a hidden SU(2) algebra that enables analytical results for Krylov complexity and fidelity. These findings, which exemplify the rare capability to characterize QMBS analytically, are feasible with current experimental techniques and offer deep insights into the nonergodic dynamics of interacting quantum systems.