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We review the methodology to theoretically treat parity-time- (PT -) symmetric, non-Hermitian quantum many-body systems. They are realized as open quantum systems with PT symmetry and couplings to the environment which are compatible. PT -symmetric non-Hermitian quantum systems show a variety of fascinating properties which single them out among generic open systems. The study of the latter has a long history in quantum theory. These studies are based on the Hermiticity of the combined system-reservoir setup and were developed by the atomic, molecular, and optical physics as well as the condensed matter physics communities. The interest of the mathematical physics community in PT -symmetric, non-Hermitian systems led to a new perspective and the development of the elegant mathematical formalisms of PT -symmetric and biorthogonal quantum mechanics, which do not make any reference to the environment. In the mathematical physics research, the focus is mainly on the remarkable spectral properties of the Hamiltonians and the characteristics of the corresponding single-particle eigenstates. Despite being non-Hermitian, the Hamiltonians can show parameter regimes, in which all eigenvalues are real. To investigate emergent quantum many-body phenomena in condensed matter physics and to make contact to experiments one, however, needs to study expectation values of observables and correlation functions. One furthermore, has to investigate statistical ensembles and not only eigenstates. The adoption of the concepts of PT -symmetric and biorthogonal quantum mechanics by parts of the condensed matter community led to a controversial status of the methodology. There is no consensus on fundamental issues, such as, what a proper observable is, how expectation values are supposed to be computed, and what adequate equilibrium statistical ensembles and their corresponding density matrices are. With the technological progress in engineering and controlling open quantum many-body systems it is high time to reconcile the Hermitian with the PT -symmetric and biorthogonal perspectives. We comprehensively review the different approaches, including the overreaching idea of pseudo-Hermiticity. To motivate the Hermitian perspective, which we propagate here, we mainly focus on the ancilla approach. It allows to embed a non-Hermitian system into a larger, Hermitian one. In contrast to other techniques, e.g., master equations, it does not rely on any approximations. We discuss the peculiarities of PT -symmetric and biorthogonal quantum mechanics. In these, what is considered to be an observable depends on the Hamiltonian or the selected (biorthonormal) basis. Crucially in addition, what is denoted as an “expectation value” lacks a direct probabilistic interpretation, and what is viewed as the canonical density matrix is non-stationary and non-Hermitian. Furthermore, the non-unitarity of the time evolution is hidden within the formalism. We pick up several model Hamiltonians, which so far were either investigated from the Hermitian perspective or from the PT -symmetric and biorthogonal one, and study them within the respective alternative framework. This includes a simple two-level, single-particle problem but also a many-body lattice model showing quantum critical behavior. Comparing the outcome of the two types of computations shows that the Hermitian approach, which, admittedly, is in parts clumsy, always leads to results which are physically sensible. In the rare cases, in which a comparison to experimental data is possible, they furthermore agree to these. In contrast, the mathematically elegant PT -symmetric and biorthogonal approaches lead to results which, are partly difficult to interpret physically. We thus conclude that the Hermitian methodology should be employed. However, to fully appreciate the physics of PT -symmetric, non-Hermitian quantum many-body systems, it is also important to be aware of the main concepts of PT -symmetric and biorthogonal quantum mechanics. Our conclusion has far reaching consequences for the application of Green function methods, functional integrals, and generating functionals, which are at the heart of a large number of many-body methods. They cannot be transferred in their established forms to treat PT -symmetric, non-Hermitian quantum systems. It can be considered as an irony of fate that these methods are available only within the mathematical formalisms of PT -symmetric and biorthogonal quantum mechanics.

We study whether neural quantum states based on multi-layer feed-forward networks can find ground states which exhibit volume-law entanglement entropy. As a testbed, we employ the paradigmatic Sachdev-Ye-Kitaev model. We find that both shallow and deep feed-forward networks require an exponential number of parameters in order to represent the ground state of this model. This demonstrates that sufficiently complicated quantum states, although being physical solutions to relevant models and not pathological cases, can still be difficult to learn to the point of intractability at larger system sizes. This highlights the importance of further investigations into the physical properties of quantum states amenable to an efficient neural representation.

Early Medieval ceramics from the UvA excavations in Leiderdorp were for a large part produced in Germany. This article puts these ceramics in a wider context.

Purpose The COVID-19 pandemic has potential to disrupt and burden the mental health care system, and to magnify inequalities experienced by mental health service users. Methods We investigated staff reports regarding the impact of the COVID-19 pandemic in its early weeks on mental health care and mental health service users in the UK using a mixed methods online survey. Recruitment channels included professional associations and networks, charities, and social media. Quantitative findings were reported with descriptive statistics, and content analysis conducted for qualitative data. Results 2,180 staff from a range of sectors, professions, and specialties participated. Immediate infection control concerns were highly salient for inpatient staff, new ways of working for community staff. Multiple rapid adaptations and innovations in response to the crisis were described, especially remote working. This was cautiously welcomed but found successful in only some clinical situations. Staff had specific concerns about many groups of service users, including people whose conditions are exacerbated by pandemic anxieties and social disruptions; people experiencing loneliness, domestic abuse and family conflict; those unable to understand and follow social distancing requirements; and those who cannot engage with remote care. Conclusion This overview of staff concerns and experiences in the early COVID-19 pandemic suggests directions for further research and service development: we suggest that how to combine infection control and a therapeutic environment in hospital, and how to achieve effective and targeted tele-health implementation in the community, should be priorities. The limitations of our convenience sample must be noted.