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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Dynamics

MP 3.8: Talk

Monday, March 18, 2024, 17:50–18:10, HL 001

Ergodicity breaking and deviation from Eigenstate Thermalisation in relativistic QFT — •Miha Srdinsek^1,2,3, Tomaz Prosen⁴, and Spyros Sotiriadis^5,6 — ¹ISCD - Sorbonne Universite — ²IMPMC - Sorbonne Universite — ³PASTEUR - Ecole Normale Superieure, PSL — ⁴Faculty of Mathematics and Physics, University of Ljubljana — ⁵Institute of Theoretical and Computational Physics, Department of Physics, University of Crete — ⁶Dahlem Center for Complex Quantum Systems, Freie Universita *t Berlin

The validity of the ergodic hypothesis in quantum systems can be rephrased in the form of the Eigenstate Thermalisation Hypothesis (ETH), a set of statistical properties for the matrix elements of local observables in energy eigenstates, which is expected to hold in any ergodic system. We test ETH in a nonintegrable model of relativistic Quantum Field Theory (QFT) using the numerical method of Hamiltonian Truncation in combination with analytical arguments based on Lorentz symmetry and Renormalisation Group theory. We find that there is an infinite sequence of eigenstates with the characteristics of Quantum Many Body Scars, that is, exceptional eigenstates with observable expectation values that lie far from thermal values, and we show that these states are one-quasiparticle states. We argue that in the thermodynamic limit the eigenstates cover the entire area between two diverging lines, the line of one-quasiparticle states, whose direction is dictated by relativistic kinematics, and the thermal average line. Our results suggest that the strong version of ETH is violated in any relativistic QFT whose spectrum admits a quasiparticle description.

Keywords: Quantum scars; Eigenstate Thermalisation Hypothesis; Quantum chaos; Sine-Gordon model