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Designing non-Hermitian real spectra through electrostatics
Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in designing them through enforcing parity-time (PT) symmetry. In this work, we exploit a lesser-known dynamical mechanism for enforcing real-spectra, and develop a comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra. Our design approach is based on a new electrostatics analogy for modified non-Hermitian bulk-boundary correspondence, where electrostatic charge corresponds to density of states and electric fields correspond to complex spectral flow. As such, Hamiltonians of any desired spectra and state localization profile can be reverse-engineered, particularly those without any guiding symmetry principles.
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Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
Chiral edge states are highly sought after as paradigmatic topological states relevant to both quantum information processing and dissipationless electron transport. Using superconducting transmon-based quantum computers, we demonstrate chiral topological propagation that is induced by suitably designed interactions, instead of flux or spin-orbit coupling. Also different from conventional 2D realizations, our effective Chern lattice is implemented on a much smaller equivalent 1D spin chain, with sequences of entangling gates encapsulating the required time-reversal breaking. By taking advantage of the quantum nature of the platform, we circumvented difficulties from the limited qubit number and gate fidelity in present-day noisy intermediate-scale quantum era quantum computers, paving the way for the quantum simulation of more sophisticated topological states on very rapidly developing quantum hardware.
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Stabilizing multiple topological fermions on a quantum computer
Using specially designed 2-fermion interactions, we demonstrate how multiple topological fermions can coexist in quantum many-body systems on a quantum computer. Our work showcases how advances in quantum algorithm implementation enable noisy intermediate-scale quantum (NISQ) devices to be exploited for topological stabilization beyond the context of single-particle topological invariants.
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Enhanced nonlinear optical response of nodal-loop materials
Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the three-dimensional Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. The semiclassical optical response of various nodal materials and toy models were studied. For the Hopf link model, we provide a geometric picture that sheds light on the effects of nodal topology and geometry of the anisotropic response surface.
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Tidal surface states as fingerprints of non-Hermitian nodal knot metals
Non-Hermitian nodal knot metals (NKMs) contain intricate complex-valued energy bands which give rise to knotted exceptional loops and new topological surface states. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their parent knots. We identify the surface state boundaries as “tidal” intersections of the complex band structure in a marine landscape analogy. Beyond topological quantities based on Berry phases, we further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.