It is possible to simulate the dynamics of a single spin-$1/2$ ($\mathsf{PT~}$ symmetric) system by conveniently embedding it into a subspace of a larger Hilbert space with unitary dynamics. Our goal is to formulate a many body generalization of this idea i.e., embedding many body non-Hermitian dynamics. As a first step in this direction, we investigate embedding of "$N$" non-interacting spin-$1/2$ ($\mathsf{PT~}$ symmetric) degrees of freedom, thereby unfolding the complex nature of such an embedding procedure. It turns out that the resulting Hermitian Hamiltonian represents a cluster of $N+1$ spin halves with "all to all", $q$-body interaction terms ($q=1,...,N+1$) in which the additional spin-$1/2$ is a part of the larger embedding space. We can visualize it as a strongly correlated central spin model with the additional spin-$1/2$ playing the role of central spin. We find that due to the orthogonality catastrophe, even a vanishing small exchange field applied along the anisotropy axis of the central spin leads to a strong suppression of its decoherence arising from spin-flipping perturbations.
We investigate the ground state and quantum dynamics of an interacting bosonic chain with the nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, the ground state can support Mott insulators in systems with noninteger filling due to the competition between nonreciprocal hopping and the on-site interaction. For the quantum dynamics, conservation laws for non-Hermitian systems manifest a stark difference from their Hermitian counterpart. In particular, for any Hermitian operator that commutes with the Hamiltonian operator, its expectation value is guaranteed to be nonconserved…
So far, topological band theory is discussed mainly for systems described by eigenvalue problems. Here, we develop a topological band theory described by a generalized eigenvalue problem (GEVP). Our analysis elucidates that non-Hermitian topological band structures may emerge for systems described by a GEVP with Hermitian matrices. The above result is verified by analyzing a two-dimensional toy model where symmetry-protected exceptional rings (SPERs) emerge although the matrices involved are Hermitian. Remarkably, these SPERs are protected by emergent symmetry, which is unique to the systems d…
We experimentally simulate in a photonic setting non-Hermitian (NH) metals characterized by the topological properties of their nodal band structures. Implementing nonunitary time evolution in reciprocal space followed by interferometric measurements, we probe the complex eigenenergies of the corresponding NH Bloch Hamiltonians, and study in detail the topology of their exceptional lines (ELs), the NH counterpart of nodal lines in Hermitian systems. We focus on two distinct types of NH metals: two-dimensional systems with symmetry-protected ELs, and three-dimensional systems possessing symmetr…
Non-Hermiticity significantly enriches the properties of topological models, leading to exotic features such as the non-Hermitian skin effects and non-Bloch bulk-boundary correspondence that have no counterparts in Hermitian settings. Its impact is particularly illustrating in non-Hermitian quasicrystals where the interplay between non-Hermiticity and quasiperiodicity results in the concurrence of the delocalization-localization transition, the parity-time (PT)-symmetry breaking, and the onset of the non-Hermitian skin effects. Here we experimentally simulate non-Hermitian quasicrystals using …
The phenomenon of charge pumping and the modern theory of electric polarization are reconsidered by analytically taking into account emergent non-Hermitian contributions. These are accounted for through the use of an extended definition of the velocity operator and are determined by means of a dynamic Hellmann-Feynman theorem (DHFT) that we derive here for the first time. The DHFT introduces generalized Berry curvatures and it is valid for calculating observables nonperturbatively, hence with results valid to all orders of the external fields. By using the extended velocity operator we rigorou…
Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- ($\cal PT$-) and anti-$\cal PT$-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian spectral singularities called exceptional points (EPs). On the other, topological and localization transitions in non-Hermitian systems reveal new phenomena, e.g., the non-Hermitian skin effect and the absence of conventional bulk-boundary correspondence. The great majority of previous studies exclusively focus on non-Hermitian Ha…
Emergent Non-Biorthogonal Born Rule at Dynamical Quantum Phase Transitions
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（北京凝聚态物理国家实验室和中国科学院物理研究所）；School of Physics and Astronomy, Lancaster University（兰开斯特大学物理与天文学院）；New Cornerstone Science Laboratory（新基石科学实验室）；Department of Physics, Xiamen University（厦门大学物理系）
Quantum degeneracy pressure (QDP) underscores the stability of matter and is arguably the most ubiquitous many-body effect. The associated Fermi surface (FS) has broad implications for physical phenomena, ranging from electromagnetic responses to entanglement entropy (EE) area law violations. Given recent fruitful studies in condensed-matter physics under effectively non-Hermitian descriptions, it becomes urgent to study how QDP and many-body interactions interplay with non-Hermitian effects. Through a prototypical critical 1D fermionic lattice with asymmetric gain/loss, a real space FS is sho…
Open classical and quantum systems with effective parity-time ($\mathcal{PT}$) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and non-reciprocal devices. And yet, how such effective $\mathcal{PT}$-symmetric non-Hermitian models emerge out of Hermitian quantum mechanics is not well understood. Here, starting from a fully Hermitian microscopic Hamiltonian description, we show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot-circuit-QED (DQD-circuit QED) set-up, which can be controllably tuned to the $\mathcal{PT}$-symm…
Time-periodic driving in the form of coherent radiation provides powerful tool for the manipulation of topological materials or synthetic quantum matter. In this paper we propose a scheme to realize non-Hermitian semimetals exhibiting exceptional rings in the spectra through Floquet engineering. A transition from a concentric pair of the rings to a dipolar pair is observed. The concentric pair carries only a quantized Berry phase while the dipolar pair possesses opposite Chern numbers in addition, signaling a topological Lifshitz transition of the Fermi surface. The transport properties of the…
By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.
We point out that two of the most important theorems of Quantum Mechanics, the Ehrenfest theorem and the Hellmann-Feynman theorem, lack in their standard form important information: there are cases where non-Hermitian boundary contributions emerge. These contributions actually appear naturally, in order for the above theorems to be valid and applicable (i.e. in multiply-connected spaces), and this occurs for physical quantities that are not represented by well-defined self-adjoint operators (such as the position operator in a periodic potential, or in general Aharonov-Bohm configurations, eith…
We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles). A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model while preserving its analytical index. We relate those spectral flows to a generalized Chern number that we show to be equal to that of the Hermitian case, provided a line gap exists. We demonstrate the homotopic invariance of both the non-Hermitian Chern number and the spectral flow index, making explicit th…
The search of topological states in non-Hermitian systems has gained a strong momentum over the last two years climbing to the level of an emergent research front. In this Perspective we give an overview with a focus in connecting this topic to others like Floquet systems. Furthermore, using a simple scattering picture we discuss an interpretation of concepts like the Hamiltonian's defectiveness, i.e. the lack of a full basis of eigenstates, crucial in many discussions of topological phases of non-Hermitian Hamiltonians.
Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian (nH) quantum systems. We propose here a circuit realization of nH Dirac and Weyl Hamiltonians subject to time-reversal invariant pseudo-magnetic field, enabling the exploration of novel nH physics. We identify the low-energy physics with a generic real energy spectrum from the nH Landau quantization of exceptional points and rings, which can avoid the nH skin effect and provides a physical example of a quasiparticle moving in the complex plane. Realistic detect…
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency sp…
Non-Hermitian descriptions of quantum matter have seen impressive progress recently, with major advances in understanding central aspects such as their topological properties or the physics of exceptional points, the non-Hermitian counterpart of critical points. Here, we use single-photon interferometry to reconstruct the non-Hermitian Kibble-Zurek mechanism and its distinct scaling behavior for exceptional points, by simulating the defect production upon performing slow parameter ramps. Importantly, we are able to realise also higher-order exceptional points, providing experimental access to …
A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed `density matrix truncation' (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understandi…
An analog of classical "hidden variables" for qubit states is presented. The states of qubit (two-level atom, spin-1/2 particle) are mapped onto the states of three classical--like coins. The bijective map of the states corresponds to the presence of correlations of random classical--like variables associated with the coin positions "up" or "down" and the observables are mapped onto quantum observables described by Hermitian matrices. The connection of the classical--coin statistics with the statistical properties of qubits is found.
Recently 't Hooft demonstrated that ``For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization''. An extension is presented here which covers quantum systems that are characterized by a complete set of mutually commuting Hermitian operators (``beables''). We introduce the symmetry of beables: any complete set of beables is as good as any other one which is obtained through a real general linear group transformation. The quantum numbers of a specific set are related to symmetry breaking initial and boundary conditions in a deter…
Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
Origin Quantum Computing Technology (Hefei) Co., Ltd.（本源量子计算技术（合肥）有限公司）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）
A practical fault-tolerant quantum computer is worth looking forward to as it provides applications that outperform their known classical counterparts. However, millions of interacting qubits with stringent criteria are required, which is intractable with current quantum technologies. As it would take decades to make it happen, exploiting the power of noisy intermediate-scale quantum(NISQ) devices, which already exist, is becoming one of current goals. Matrix exponentiation, especially hermitian matrix exponentiation, is an essential element for quantum information processing. In this article,…
Simulating quantum phenomena in extreme spacetimes in the laboratory represents a powerful approach to explore fundamental physics in the interplay of quantum field theory and general relativity. Here we propose to simulate the movement of a Dirac particle propagating with a superluminal velocity caused by the emergent Alcubierre warp drive spacetime using trapped ions. We demonstrate that the platform allows observing the tilted lightcone that manifests as a superluminal velocity, which is in agreement with the prediction of general relativity. Furthermore, the Zitterbewegung effect arising f…
