Measurement and Feedback Driven Entanglement Transition in the Probabilistic Control of Chaos.

We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and uncontrolled phases as a function of the rate at which the control is applied. We show that such control transitions persist in open quantum systems where control is implemented with local measurements and unitary feedback. Starting from a simple classical model with a known control transition, we define a quantum model that exhibits a diffusive transition between a chaotic volume-law entangled phase and a disentangled controlled phase. Unlike other entanglement transitions in monitored quantum circuits, this transition can also be probed by correlation functions without resolving individual quantum trajectories.

Current- and Field-Induced Topology in Twisted Nodal Superconductors.

We show that interlayer current induces topological superconductivity in twisted bilayers of nodal superconductors. A bulk gap opens and achieves its maximum near a "magic" twist angle θ_{MA}. Chiral edge modes lead to a quantized thermal Hall effect at low temperatures. Furthermore, we show that an in-plane magnetic field creates a periodic lattice of topological domains with edge modes forming low-energy bands. We predict their signatures in scanning tunneling microscopy. Estimates for candidate materials indicate that twist angles θ∼θ_{MA} are optimal for observing the predicted effects.

Magnetic Weyl Semimetallic Phase in Thin Films of Eu_{2}Ir_{2}O_{7}.

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu_{2}Ir_{2}O_{7} high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Weyl Semimetal to Metal Phase Transitions Driven by Quasiperiodic Potentials.

We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentials. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an "inverted" semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Weyl point. The critical properties of the transitions in quasiperiodic systems differ from those in random systems: we do not find a clear critical scaling regime in energy; instead, at the quasiperiodic transitions, the density of states appears to jump abruptly (and discontinuously to within our resolution).

Remnant Geometric Hall Response in a Quantum Quench.

Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Here, we unveil how out-of-equilibrium states, prepared via a quantum quench in a two-band system, can exhibit a nonzero Hall-type current-a remnant Hall response-even when the instantaneous Hamiltonian is time reversal symmetric (in contrast to equilibrium Hall currents). Interestingly, the remnant Hall response arises from the coherent dynamics of the wave function that retain a remnant of its quantum geometry postquench, and can be traced to processes beyond linear response. Quenches in two-band Dirac systems are natural venues for realizing remnant Hall currents, which exist when either mirror or time-reversal symmetry are broken (before or after the quench). Its long time persistence, sensitivity to symmetry breaking, and decoherence-type relaxation processes allow it to be used as a sensitive diagnostic of the complex out-of-equilibrium dynamics readily controlled and probed in cold-atomic optical lattice experiments.

Statistical mechanics of stochastic quantum control: d-adic Rényi circuits.

The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic d-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.

Breakdown of the coherent state path integral: two simple examples.

We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin-path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.

Controllable quantum point junction on the surface of an antiferromagnetic topological insulator.

Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.