We review how tensor networks are used in quantum field theory on the lattice. The striking feature of the method is free of the sign problem which is a serious drawback of the Monte Carlo method. In fact the tensor networks have been applied and verified mainly in two dimensional system. On the other hand, the computation cost of the tensor networks is known to be severe for higher dimensional system. Recently, however, thanks to the progress of the coarse-graining algorithm, tensor network studies of the four dimensional system with simple internal degree of freedom have just started. We hope that further algorithmic developments make the tensor network computation of lattice QCD feasible.
Unconventional symmetry breaking without spin order, such as the rotational symmetry breaking (=nematic or smectic) orders as well as the spontaneous loop-current orders, have been recently reported in cuprate superconductors and their related materials. They are theoretically represented by the non-A1g particle-hole condensation. In this paper, we analyze typical Hubbard models by applying the renormalization-group method and the density-wave equation method, and find that various unconventional orderings emerge due to the quantum interference among spin fluctuations.
We report on the observations of cosmic gamma rays in the 100 TeV energy region with new hybrid detectors consisting of the surface scintillation detectors combined with the underground water-Cherenkov-type muon detectors. The highest energy of the detected gamma rays from the Crab Nebula is estimated to be unprecedentedly as high as 450 TeV. We also detected gamma rays beyond 100 TeV from the overlapping region between SNR G106.3+2.7 and the molecular cloud. This feature suggests that SNR G106.3+2.7 is a potential candidate for a PeVatron, which is the cosmic-ray accelerator beyond PeV energies existing in our Galaxy. Our observations open a new energy window (beyond 100 TeV) in the gamma-ray astronomy and astrophysics.
The behavior of the entropy of the Hawking radiation is investigated by the gravitational path-integral. It is calculated using the replica spacetimes that consist of n-copies of the original spacetime. We found that a wormhole connecting different copies of the spacetime gives an important contribution to the entropy at late stages of the black hole evaporation. It reproduces the so-called Page curve, suggesting that an evaporating black hole obeys the unitary time evolution.