Condensed Matter Theory

Abstract:

We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. We identify the regime in which the diagonal approximation holds and the nature of the leading corrections to it. We focus on the behavior of the spectral form factor (SFF) and of matrix elements of local operators, averaged over an ensemble of random circuits, making comparisons with the predictions of random matrix theory (RMT) and the eigenstate thermalization hypothesis (ETH). We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these contributions consist of many spatial domains, with distinct local pairings in neighboring domains. The existence of these domains is reflected in deviations of the SFF from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged SFF. In addition, we find that domains of a second type control non-Gaussian fluctuations of the SFF. These domains are separated by walls that are related to the entanglement membrane, known to characterize the scrambling of quantum information.

Abstract:

We prove that the boundaries of all nontrivial (1+1)-dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or antiunitary), are supersymmetric quantum mechanical systems. This supersymmetry does not require any fine-tuning of the underlying Hamiltonian, arises entirely as a consequence of the boundary 't Hooft anomaly that classifies the phase, and is related to a "Bose-Fermi" degeneracy different in nature from other well known degeneracies such as Kramers doublets.

Abstract:

Bacterial biofilms are communities of bacteria that exist as aggregates that can adhere to surfaces or be free-standing. This complex, social mode of cellular organization is fundamental to the physiology of microbes and often exhibits surprising behavior. Bacterial biofilms are more than the sum of their parts: single-cell behavior has a complex relation to collective community behavior, in a manner perhaps cognate to the complex relation between atomic physics and condensed matter physics. Biofilm microbiology is a relatively young field by biology standards, but it has already attracted intense attention from physicists. Sometimes, this attention takes the form of seeing biofilms as inspiration for new physics. In this roadmap, we highlight the work of those who have taken the opposite strategy: we highlight the work of physicists and physical scientists who use physics to engage fundamental concepts in bacterial biofilm microbiology, including adhesion, sensing, motility, signaling, memory, energy flow, community formation and cooperativity. These contributions are juxtaposed with microbiologists who have made recent important discoveries on bacterial biofilms using state-of-the-art physical methods. The contributions to this roadmap exemplify how well physics and biology can be combined to achieve a new synthesis, rather than just a division of labor.