We study signatures of quantum chaos in (1+1)D Quantum Field Theory (QFT) models. Our analysis is based on the method of Hamiltonian truncation, a numerical approach for the construction of low-energy spectra and eigenstates of QFTs that can be considered as perturbations of exactly solvable models. We focus on the double sine-Gordon, also studying the massive sine-Gordon and φ 4 model, all of which are non-integrable and can be studied by this method with sufficiently high precision from small to intermediate perturbation strength. We analyse the statistics of level spacings and of eigenvector components, which are expected to follow Random Matrix Theory predictions. While level spacing statistics are close to the Gaussian Orthogonal Ensemble as expected, on the contrary, the eigenvector components follow a distribution markedly different from the expected Gaussian. Unlike in the typical quantum chaos scenario, the transition of level spacing statistics to chaotic behaviour takes place already in the perturbative regime. Moreover, the distribution of eigenvector components does not appear to change or approach Gaussian behaviour, even for relatively large perturbations. Our results suggest that these features are independent of the choice of model and basis.
The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the Rényi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the Rényi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the φ 4 model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes -para, disordered and quasi long-range ordered -, met as the interaction is increased. The Rényi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the Rényi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all φ 4 -like systems, as well as in the elusive water ice transition across phases VII, VIII and X.
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