Lee-Yang theory of the two-dimensional quantum Ising model

Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range of problems such as the understanding and design of quantum materials. For classical equilibrium systems, the Lee-Yang formalism provides a rigorous foundation of phase transitions, and these ideas have also been extended to the quantum realm. Here, we develop a Lee-Yang theory of quantum phase transitions that can include thermal fluctuations caused by a finite temperature, and it thereby provides a link between the classical Lee-Yang formalism and recent theories of phase transitions at zero temperature. Our methodology exploits analytic properties of the moment generating function of the order parameter in systems of finite size, and it can be implemented in combination with tensor-network calculations. Specifically, the onset of a symmetry-broken phase is signaled by the zeros of the moment generating function approaching the origin in the complex plane of a counting field that couples to the order parameter. Moreover, the zeros can be obtained by measuring or calculating the high cumulants of the order parameter. We determine the phase diagram of the two-dimensional quantum Ising model and thereby demonstrate the potential of our method to predict the critical behavior of two-dimensional quantum systems at finite temperatures.Comment: 10 pages, 6 figure

Lee-Yang theory of quantum phase transitions with neural network quantum states

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.Comment: 10 pages, 6 figures, 1 tabl

Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological invariants. In particular, we express the three-dimensional winding number of point-gapped non-Hermitian systems, which is defined as an integral over the whole Brillouin zone, in terms of symmetry eigenvalues at high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian topological insulators, we find that symmetry indicators characterize the associated Chern-Simons form, whose evaluation usually requires a computationally expensive choice of smooth gauge. In each case, we discuss the non-Hermitian surface states associated with nontrivial symmetry indicators.Comment: 6 pages, 1 figure, supplement include

Special behavior of alkali beam emission spectroscopy in low-ion-temperature plasma

Beam emission spectroscopy (BES) is a powerful plasma diagnostic method especially suited for the measurement of plasma density and its fluctuations. As such, synthetic BES codes are regularly used to aid the design or utilization of these diagnostic systems. However, synthetic diagnostics can also be used to study the method in previously not yet explored operational conditions. This paper presents such an analysis utilizing the RENATE-OD synthetic diagnostic code for a hypothetical alkali BES system on the HSX stellarator. HSX is a device featuring an unusual operating regime in the world of fusion devices due to the low ion temperature and low plasma density. It was found that BES shows unusual tendencies in these conditions. The relation between beam energy and plasma penetration in low-ion-temperature plasma, together with unique emission features facilitated by low-density plasma, and the underlying reasons behind these features are explored in this paper

Statistical analysis of plasma filaments in the island divertor of Wendelstein 7-X

Plasma filaments have been measured with alkali beam emission spectroscopy in the plasma edge, divertor island, and scrape-off layer of Wendelstein 7-X. Due to the high intensity of a 1–2 kHz plasma mode, a new, correlation based conditional averaging algorithm was used to search for filaments in the signals. With that method, effects of different magnetic configurations and density levels on filament properties are observed. In configurations where the islands are small and do not play an important role for the connection length topology, filaments behave similar to tokamaks. In contrast, in configurations with larger magnetic islands and more complex connection length profiles, filaments behave quite differently, for instance they may or may not appear in the inner side of the divertor island depending on the plasma parameters. Coupling between the filaments and lower frequency events are also showed. The role of filaments in the global and local particle transport is briefly discussed