In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling"is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.
In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.
We study the two point correlation function of a local operator on an \(n\)-sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. We calculate the Renyi transform in \(2d\) conformal field theories, and use it to extract the off-diagonal elements of (modular) ETH.
Critical drag is thus a mechanism for resistivity that, unlike conventional mechanisms, is unrelated to broken symmetries. We furthermore argue that an emergent symmetry that has the appropriate mixed anomaly with electric charge is in fact an inevitable consequence of compressibility in systems with lattice translation symmetry. Critical drag therefore seems to be the only way (other than through irrelevant perturbations breaking the emergent symmetry, that disappear at the renormalization group fixed point) to get nonzero resistivity in such systems. Finally, we present a very simple and concrete model -- the "Quantum Lifshitz Model" -- that illustrates the critical drag mechanism as well as the other considerations of the paper.
The study of topological superconductivity is largely based on the analysis of mean-field Hamiltonians that violate particle number conservation and have only short-range interactions. Although this approach has been very successful, it is not clear that it captures the topological properties of real superconductors, which are described by number-conserving Hamiltonians with long-range interactions. To address this issue, we study topological superconductivity directly in the number-conserving setting.