The Broken Symmetry of Time

Zack Savitsky

Jasper van Wezel

The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.

Felix M. Lev

Daniel E. Parker, Romain Vasseur, Thomas Scaffidi

We argue that symmetry-broken phases proximate in phase space to symmetry-protected topological phases can exhibit dynamical signatures of topological physics. This dynamical, symmetry-protected "topological" regime is characterized by anomalously long edge coherence times due to the topological decoration of quasiparticle excitations, even if the underlying zero-temperature ground state is in a nontopological, symmetry-broken state. The dramatic enhancement of coherence can even persist at infinite temperature due to prethermalization. We find exponentially long edge coherence times that are stable to symmetry-preserving perturbations and not the result of integrability.

J. G. Cramer

Riku Tuovinen, Denis Golež, Michael Schüler +3 more

A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff–Baym Ansatz (GKBA) is applied to a lattice system with a symmetry‐broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetry‐broken initial state from a Hartree– Fock wave function within GKBA is assessed by comparing with a solution of the imaginary‐time Dyson equation. It is found that it is possible to reach a symmetry‐ broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.