Thermalization and chaos in a 1+1d QFT

Abstract

We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors.

17 pages, 18 figures; v2: added Fig.10 on quantum scars, published version

References in corpus (4)

• Thermalization and its mechanism for generic isolated quantum systems
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Gravitational orbits, double-twist mirage, and many-body scars
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory

Cited by in corpus (13)

• Scrambling is Necessary but Not Sufficient for Chaos
• Quantum state complexity meets many-body scars
• Holographic Quantum Scars
• Constructing the Infrared Conformal Generators on the Fuzzy Sphere
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• Towards a nonperturbative construction of the $S$-matrix
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Fast quantum state preparation and bath dynamics using non-Gaussian variational ansatz and quantum optimal control
• Quantum Scars in Quantum Field Theory
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Ergodicity breaking and deviation from Eigenstate Thermalisation in relativistic QFT
• Weak vs. strong breaking of integrability in interacting scalar quantum field theories
• Universal thermalization dynamics in (1+1)d QFTs