Theory of robust quantum many-body scars in long-range interacting systems

Abstract

Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work we demonstrate that long-range interacting quantum spin systems generically host robust QMBS. We analyze spectral properties upon raising the power-law decay exponent $\alpha$ of spin-spin interactions from the solvable permutationally-symmetric limit $\alpha =0$. First, we numerically establish that despite spectral signatures of chaos appear for infinitesimal $\alpha$, the towers of $\alpha =0$ energy eigenstates with large collective spin are smoothly deformed as $\alpha$ is increased, and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor non-linearly coupled to an extensive set of bosonic modes. We analitycally solve for the eigenstates of this interacting impurity model by means of a novel polaron-type canonical transformation, and show their self-consistent localization in large-spin sectors of the original Hamiltonian for $0<\alpha <d$ (with $d$ = spatial dimension of the lattice). Our theory unveils the stability mechanism of such QMBS for arbitrary system size and predicts instances of its breakdown, e.g. near dynamical critical points or in presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a byproduct, we find a predictive criterion for presence or absence of heating under periodic driving for $0<\alpha <d$, beyond existing Floquet-prethermalization theorems.

26+14 pages, 15+3 figures. Corrected several misprints in text and figures. Version accepted in Physical Review X

References in corpus (39)

• Probing many-body dynamics on a 51-atom quantum simulator
• Localization of interacting fermions at high temperature
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Dipolar physics: A review of experiments with magnetic quantum gases
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Excited state quantum phase transitions in many-body systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Many-body localization dynamics from gauge invariance
• Dynamics in many-body localized quantum systems without disorder
• Excited-state quantum phase transitions
• Diverging equilibration times in long-range quantum spin models
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Chaos, entanglement and decoherence in the quantum kicked top
• Impact of Quantum Phase Transitions on Excited Level Dynamics
• On quantum mean-field models and their quantum annealing
• Exact many-body scars and their stability in constrained quantum chains
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Entanglement and chaos in the kicked top
• Entanglement enhanced metrology with quantum many-body scars
• Superdiffusive Energy Transport in Kinetically Constrained Models
• Genuine many-body quantum scars along unstable modes in Bose-Hubbard systems
• Quantum many-body scars in bipartite Rydberg arrays originate from hidden projector embedding
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• Quantum Entanglement dependence on bifurcations and scars in non autonomous systems. The case of Quantum Kicked Top
• Combined use of translational and spin-rotational invariance for spin systems
• Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space
• Asymptotic Quantum Many-Body Scars
• Quantum Many-Body Scars in Dual-Unitary Circuits
• Bridging quantum criticality via many-body scarring
• Quantum bounds on the generalized Lyapunov exponents
• Fractal nature of high-order time crystal phases
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects
• Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models
• Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains
• Rotor/spin-wave theory for quantum spin models with U(1) symmetry
• Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects

Cited by in corpus (8)

• Proposal for many-body quantum chaos detection
• Hydrodynamics and the eigenstate thermalization hypothesis
• Spectral form factor and energy correlations in banded random matrices
• Ensemble Inequivalence in Long-Range Quantum Spin Systems
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays
• Floquet thermalization by power-law induced permutation symmetry breaking
• Tighter thermalization bounds for perturbed quantum many-body scars