University of ljubljana faculty of mathematics and physics department of physics mathematical physics

Classical concepts in the theory of dynamical systems, like integrability, periodicity, and chaos, were observed to have quantum analogues, which is re ected in the di erence of spectral properties. Although the statement is well-grounded in evidence, we are lacking veri cations to a large extent in models of quantum eld theory. With the help of the Truncated Conformal Space Approach (TCSA) we investigate spectral properties of non-integrable relativistic (1+1)D models of quantum eld theory de ned on nite space. We study the distributions of level spacings and the distribution of ratios of consecutive level spacings, both of which are well established in literature as good signatures of quantum chaos. The models we study include the φ, double sine-Gordon, massive Schwinger-Thirring model, and the integrable sine-Gordon model for comparison. We develop a conservative measure of truncation error that estimates the convergence of spectral statistics, and by increasing the integrability breaking parameters we observe a gradual onset of statistics predicted by quantum chaos theory the statistics of random matrices. Surprisingly, we observe a strong quantum integrability breaking already at small system sizes, and by extrapolation we estimate that quantum chaos can be observed also at an in nite system size. At the same time, by studying the diagonal elements of observables in the energy eigenbasis of non-integrable models, we nd preliminary evidence that the Eigenstate Thermalization Hypothesis is obeyed. The results presented in the thesis show that the TCSA can be used for analysing quantum chaos in (1+1)D models of quantum eld theory, reveal that signatures of quantum chaos indeed appear in continuous quantum models as well, and unveil non-trivial properties of the parameter space of the investigated theories.