The Kibble Zurek mechanism describes the universal formation of topological defects during continuous symmetry breaking phase transitions. It has been confirmed in a wide variety of systems and is of interest within theoretical high energy physics and cosmology. While during high temperature phase transitions classical methods can be used to study topological defect formation, in zero temperature quantum phase transitions, quantum effects can dominate dynamics such that classical approximations fail. This is problematic in quantum field theory because topological defect formation constitutes a non-perturbative non-equilibrium phenomenon, yet there are at present no well-developed non-perturbative non-equilibrium methods available for calculations. Nonetheless, due to its generality and confirmation in other cases, the Kibble-Zurek mechanism is expected to hold. This means that in addition to being of physical interest in its own right, the Kibble-Zurek mechanism is also an excellent test for any potential non-perturbative non-equilibrium techniques. In this thesis, tensor network techniques are applied to the problem of confirming the Kibble Zurek mechanism in the phi^4 quantum field theory in D = (1 + 1) spacetime dimensions. Such techniques have already been highly successful in condensed matter and to some extent in quantum field theory. The kink defects of the theory are studied both in equilibrium and in the non-equilibrium scenario of their formation. Results consistent with the Kibble-Zurek mechanism are found, which provides evidence that the mechanism holds in this case and confirms tensor networks as a promising non-perturbative non-equilibrium method for quantum field theory. As tensor network methods are developed further to higher dimensions and more sophisticated theories, they could one day provide a powerful method for the non-perturbative study of non-equilibrium high energy physics and cosmology, an area of physics which remains essentially unexplored yet important for our understanding of nature.
The Kibble Zurek mechanism in a relativistic ${\ensuremath{\phi}}^{4}$ scalar field theory in
D=(1+1) is studied using uniform matrix product states. The equal time two point function in momentum space
G2(k) is approximated as the system is driven through a quantum phase transition at a variety of different quench rates ${\ensuremath{\tau}}_{Q}$. We focus on looking for signatures of topological defect formation in the system and demonstrate the consistency of the picture that the two point function
G2(k) displays two characteristic scales, the defect density
n and the kink width
dK. Consequently,
G2(k) provides a clear signature for the formation of defects and a well defined measure of the defect density in the system. These results provide a benchmark for the use of tensor networks as powerful nonperturbative nonequilibrium methods for relativistic quantum field theory, providing a promising technique for the future study of high energy physics and cosmology.
Abstract We study the dynamics of second-order phase transitions that may have taken place in the early universe and analyze the Kibble-Zurek (KZ) scaling as well as the formation of topological defects emerging from a quench in the one-dimensional Bose-Hubbard model. We describe the universal dynamics of the KZ mechanism (KZM) and the topological defect formation by simulating the Bose–Hubbard model at zero temperature. We study the effects of thermalization on the ground state by analyzing the transition between Mott and superfluid phases. The out-of-equilibrium dynamics induced by a quench of the hopping parameter is presented. We find a KZ scaling behaviour at zero temperature and analyze the KZ dynamics.
Systems passing through quantum critical points at finite rates have a finite probability of undergoing transitions between different eigenstates of the instantaneous Hamiltonian. This mechanism was proposed by Kibble as the underlying mechanism for the formation of topological defects in the early universe and by Zurek for condensed matter systems. Here, we use a system of nuclear spins as an experimental quantum simulator undergoing a non-equilibrium quantum phase transition. The experimental data confirm the validity of the Kibble–Zurek mechanism of defect formation.
We investigate the out-of-equilibrium dynamics of a relativistic
Z2-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature
Tc. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near
Tc this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures
T≪Tc nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for
T≲Tc, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.
In context of the search for the QCD critical endpoint in heavy-ion collisions, a deep understanding of the out-of-equilibrium dynamics of the system is necessary to make well-grounded predictions for signatures in final states. To this end, we investigate the dynamic critical behavior of a classical scalar field theory with
Z2 symmetry in the dynamic universality class of Model A in two spatial dimensions. The critical dynamics of the system is studied under a linear quench protocol, in which the external symmetry breaking field is changed at a constant rate through the critical point. We discuss the connection to the Kibble-Zurek mechanism and determine universal scaling functions, which fully describe the non-equilibrium evolution of the system near the critical point for all quench rates under consideration. We find that, while the scaling functions are non-trivial, the corresponding scaling exponents are fully determined by static critical exponents and the dynamic critical exponent.