Continuous fields (or bundles) of
C∗-algebras form an important ingredient for describing emergent phenomena, such as phase transitions and spontaneous symmetry breaking. In this work, we consider the continuous
C∗-bundle generated by increasing symmetric tensor powers of the complex
ℓ×ℓ matrices
Mℓ(C), which can be interpreted as abstract description of mean-field theories defining the macroscopic limit of infinite quantum systems. Within this framework we discuss the principle of large deviations for the local Gibbs state in the high temperature regime and characterize the limit of the ensuing logarithmic generating function.
We study the statistics of large deviations of the intensive work done in an interaction quench of a one-dimensional Bose gas with a large number N of particles, system size L, and fixed density. We consider the case in which the system is initially prepared in the noninteracting ground state and a repulsive interaction is suddenly turned on. For large deviations of the work below its mean value, we show that the large-deviation principle holds by means of the quench action approach. Using the latter, we compute exactly the so-called rate function and study its properties analytically. In particular, we find that fluctuations close to the mean value of the work exhibit a marked non-Gaussian behavior, even though their probability is always exponentially suppressed below it as L increases. Deviations larger than the mean value exhibit an algebraic decay whose exponent cannot be determined directly by large-deviation theory. Exploiting the exact Bethe ansatz representation of the eigenstates of the Hamiltonian, we calculate this exponent for vanishing particle density. Our approach can be straightforwardly generalized to quantum quenches in other interacting integrable systems.