Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory.

A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)-a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-[Formula: see text] Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds.

Multiscale structural complexity of natural patterns.

Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects.

Generalization properties of neural network approximations to frustrated magnet ground states.

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.