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We identify and investigate two classes of non-Hermitian systems, i.e., one resulting from Lorentz-symmetry violation (LSV) and the other from a complex mass (CM) with Lorentz invariance. The mechanisms to break, and approaches to restore, the bulk-boundary correspondence in these two types of non-Hermitian systems are clarified. The non-Hermitian system with LSV shows a non-Hermitian skin effect, and its topological phase can be characterized by mapping it to the Hermitian system via a non-compact U (1) gauge transformation. In contrast, there exists no non-Hermitian skin effect for the non-Hermitian system with CM. Moreover, the conventional bulk-boundary correspondence holds in this (CM) system. We also consider a general non-Hermitian system in the presence of both LSV and CM, and we generalize its bulk-boundary correspondence. * yrzhang@csrc.ac.cn † tao.liu@riken.jp ‡ hfan@iphy.ac.cn Hamiltonians, usually fail to characterize topological phases in non-Hermitian systems, which leads to the breakdown of the conventional bulk-boundary correspondence. Although many efforts have been made to propose new topological invariants, e.g. non-Bloch winding and Chern numbers [92,93], to restore the bulk-boundary correspondence of non-Hermitian Hamiltonians [92][93][94][95][96], it remains a challenge to understand and characterize the topological phases of non-Hermitian systems. For example, for a non-Hermitian Hamiltonian, should its topological phase follow the Block-wave or non-Blochwave behavior? This is not uncovered in Refs. [92,93].In this paper, we investigate the topological phases of non-Hermitian systems. According to both Dirac and current-conservation equations, non-Hermitian systems can mainly be classified into two classes: one resulting from Lorentz symmetry violation (LSV), and the other from a complex mass (CM) with Lorentz invariance. We clarify the mechanisms to break the conventional bulk-boundary correspondence in these two types of non-Hermitian systems, and develop approaches to generalize the bulk-boundary correspondence.In particular, the topological phases of non-Hermitian Hamiltonians with LSV can be described by non-Bloch topological invariants, while those with CM follow the Blochwave behavior. The non-Hermitian Su-Schrieffer-Heeger (SSH) [97], Qi-Wu-Zhang (QWZ) [98] models and the disordered Kitaev chain [3] exemplify our approaches. Remarkably, our approach can unperturbatively predict the topological phases of 2D non-Hermitian systems. We also discuss a general non-Hermitian system containing both LSV and CM non-Hermiticities.The remaining of this paper is organized as follows. In Sec. II, we give a short review of Hermitian Dirac arXiv:1903.09985v2 [cond-mat.mes-hall]

Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical computers. While quantum computers hold the promise of solving this problem more efficiently in the long run, existing quantum algorithms requiring deep quantum circuits are infeasible for near-term noisy quantum processors. Herein, we introduce a pragmatic variational quantum response (VQR) algorithm for response properties, which circumvents the need for deep quantum circuits. Using this algorithm, we report the first simulation of linear response properties of molecules including dynamic polarizabilities and absorption spectra on a superconducting quantum processor. Our results indicate that a large class of important dynamical properties, such as Green’s functions, are within the reach of near-term quantum hardware using this algorithm in combination with suitable error mitigation techniques.

The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic XY spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.

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We report on controllable cavity modes by controlling the backscattering by two identical scatterers. Periodic changes of the backscattering coupling between two degenerate cavity modes are observed with the changing angle between two scatterers and elucidated by a theoretical model using two-mode approximation and numerical simulations. The periodically appearing single-peak cavity modes indicate mode degeneracy at diabolical points. Interactions between single quantum dots and cavity modes are then investigated. Enhanced emission of a quantum dot with a six-fold intensity increase is obtained in a microdisk at a diabolical point. This method to control cavity modes allows large-scale integration, high reproducibility and flexible design of the size, the location, the quantity and the shape for scatterers, which can be applied for integrated photonic structures with scatterer-modified light-matter interaction.

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