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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - NpQFT-NEq (New non perturbative methods for out-of-equilibrium quantum field theory)

Teaser

Summary

Understanding the non-equilibrium dynamics of quantum systems of many particles is a challenge that permeates all areas of modern physics. Whether in particle accelerator experiments, or in the development of new materials, one often encounters the problem of having a large number of particles which interact quantum mechanically with each other. If one smashes together clusters of particles (as is done in nuclear collisions), or suddenly disturbs, periodically kicks or induces currents, the system becomes unstable, and loses equilibrium. The interactions between particles when driven out of equilibrium, give rise to intricate collective phenomena.

In this project, we worked on developing and applying new theoretical techniques to study such non-equilibrium systems. The focus is in particular on quantum field theories, where the system may be described as a continuum rather than a discrete set of particles. We made significant progress by considering low-dimensional models which often can be solved exactly, providing an ideal platform to probe and understand non-equilibrium dynamics in a rigorous manner.

Work performed

One major result of this project is the formulation of the Thermodynamic Bootstrap Program for integrable quantum field theories. This is a new analytic framework that allows us to compute finite-temperature and non-equilibrium correlation functions and physical observables in an axiomatic self-consistent manner.

A significant part of our project was dedicated to understanding the behavior of quantum field theories after a quantum quench, where some parameter of the system is suddenly changed, pushing the system out of equilibrium. One important result was the formulation of a time-dependent effective central charge, a quantity which is related to the number of degrees of freedom of the system. This quantity allowed us to understand quenches where the pre- and post-quench systems have a different number of effective degrees of freedom. Also along the line of quantum quenches, we have elucidated the role that the existence of particle bound states has on the late-time dynamics of physical observables.

Other results include understanding a limited form of integrability that can survive even in periodically driven systems. We have also found analytic evidence for lack of thermalization in non-integrable theories which exhibit particle confinement. Finally, we have found surprising applications of concepts from non-equilibrium integrable systems, in the formulation of quantum machine learning algorithms.

Final results

Arguably the result of this project which most pushes the state of the art is the formulation of the Thermodynamic Bootstrap Program (TBP). While it has been known for many years how to systematically compute ground-state correlation functions in integrable field theories, the generalization to finite-temperature correlation functions has been an ongoing problem for more than two decades. The TBP not only provides a new viable path to compute such thermal correlation functions, but it opens the door to a vast exploration into non-equilibrium physics.

The TBP allows one to study field theories where an extensive amount of energy has been pumped into the system, describing not only thermal equilibrium, but non-equilibrium settings, such as quantum quenches, and more recently, spatially inhomogeneous quenches which have been studied through a generalized hydrodynamical formalism. The TBP has been shown to be consistent with independent predictions from generalized hydrodynamics, yet also the TBP provides a path to systematically perturb away from the hydrodynamical limit.

Some of the other innovative results of this project have been fueled by interdisciplinary collaboration. For instance, our results on the thermalization properties of confining gauge field theories provides valuable insights for high energy physics. Perhaps the most surprising interdisciplinary application to come out of this project was the introduction of generalized-Gibbs-ensemble based quantum machine learning algorithms. This approach uses knowledge of quantum quenches of integrable models to design the simplest possible quantum Boltzmann machine, i.e. the quantum machine with the shortest theoretically possible training time.