Theory of robust ergodicity breaking in quantum many-body systems with long-range interactions
Alessio Lerose (University of Oxford)
Recent years have seen the discovery of a number of routes to (strong or weak forms of) ergodicity breaking in isolated quantum many-body systems, even in absence of quenched disorder. Quantum many-body scars (QMBS) – exceptional energy eigenstates associated with violations of thermalization for special non-equilibrium initial states – rank as a novel remarkable possibility. The various systematic constructions of QMBS, however, require fine-tuning of local Hamiltonian parameters. In this talk I will demonstrate that long-range interacting quantum spin lattices generically host robust QMBS. This result is based on an analysis of spectral properties upon raising the power-law decay exponent α of spin-spin interactions from the solvable permutationally-symmetric limit α=0:
- Firstly we numerically establish that, despite spectral signatures of quantum chaos appear for infinitesimal α, the towers of α=0 energy eigenstates with large collective spin are smoothly deformed as α is increased, and exhibit characteristic QMBS features.
- To elucidate the nature and fate of these states in larger systems we introduce a novel analytical approach based on mapping the quantum spin Hamiltonian onto a relativistic quantum rotor non-linearly coupled to an extensive set of bosonic modes. We provide an original exact solution for the eigenstates of this interacting impurity model, and show their self-consistent localization in large-spin sectors of the original spin Hamiltonian for 0<α<d.
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 absence of heating under periodic driving beyond existing Floquet-prethermalization theorems. I will finally briefly discuss how the multipartite entanglement structure of the persistent non-equilibrium states discovered here has potential metrological applications in present-day experimental platforms.
Main Ref: https://arxiv.org/abs/2309.12504