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Abstract:

From the birth of galaxies to the self-organizing dynamics of our planet to the ongoing expansion of the universe, the more we discover about the evolution of the cosmos, the more acutely we realize the enormity of what remains to be known. Just this year astrophysicists at the University of Nottingham confirmed that there are at least two trillion galaxies in the cosmos, 10 times more than had been previously thought. What guidance or wisdom can the study of cosmology and astrophysics offer us in our search for meaning and purpose? In conversation with Steve Paulson, executive producer and host of To the Best of Our Knowledge, theoretical physicists Paul Davies and Ard Louis, and astrophysicist Lucianne Walkowicz share their perceptions based on years of gazing upward and beyond our own intimate planet.

Abstract:

We study the nonequilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian D 3 symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the Z 3 clock symmetry or a Z 2 chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.

Abstract:

We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor $K(t)$ analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, $t_{\rm Th}$. We obtain a striking dependence of $t_{\rm Th}$ on the spatial dimension $d$ and size of the system. For $d>1$, $t_{\rm Th}$ is finite in the thermodynamic limit and set by the inter-site coupling strength. By contrast, in one dimension $t_{\rm Th}$ diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form.