Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model

The helicity modulus of the S=1/2 XY model is precisely estimated through a world line quantum Monte Carlo method enhanced by a cluster update algorithm. The obtained estimates for various system sizes and temperatures are well fitted by a scaling form with L replaced by \log(L/L_0), which is inferred from the solution of the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.Comment: 4 pages, 3 figure

SU(N) Heisenberg model with multi-column representations

The $\mathrm{SU}(N)$ symmetric antiferromagnetic Heisenberg model with multi-column representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of Young diagram with two columns, we confirm that a valence-bond solid order appears as soon as the N\'eel order disappears at $N = 10$ indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for both of the N\'eel and the valence-bond solid ordering for $N\ge 15$. This is actually consistent with the large-$N$ theory, which predicts that the VBS state immediately follows the N\'eel state, because the expected spontaneous order is too weak to be detected.Comment: 5 pages, 5 figure

Entropy Governed by the Absorbing State of Directed Percolation

We investigate the informational aspect of (1+1)-dimensional directed percolation, a canonical model of a nonequilibrium continuous transition to a phase dominated by a single special state called the "absorbing" state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of directed percolation. We find a universal relaxation of Renyi entropy at the absorbing phase transition point as well as a new singularity in the active phase, slightly but distinctly away from the absorbing transition point. At the new singular point, the second-order Renyi entropy has a clear cusp. There we also detect a singular behavior of "entanglement entropy," defined by regarding the probability distribution as a wave function. The entanglement entropy vanishes below the singular point and stays finite above. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time evolution of the Renyi entropy at the critical point as well as in the active phase.Comment: 8(=4+4)pages, 13(=5+6) figure

FOREVER22: Gas and metal outflow from massive galaxies in protocluster regions

We study gas and metal outflow from massive galaxies in protocluster regions at $z=3-9$ by using the results of the FOREVER22 simulation project. Our simulations contain massive haloes with $M_{\rm h} \gtrsim 10^{13}~\rm M_{\odot}$, showing high star formation rates of $> 100~\rm M_{\odot}~yr^{-1}$ and hosting supermassive black holes with $M_{\rm BH} \gtrsim 10^{8}~\rm M_{\odot}$. We show that the mass loading factor ($\eta_{\rm M}$) sensitively depends on the halo mass and it is $\eta_{\rm M} = 1.2~(9.2)$ for $M_{\rm h} = 10^{13}~(10^{11})~\rm M_{\odot}$. Once the halo mass exceeds $\sim 10^{12.5}~\rm M_{\odot}$, the outflow velocity of the gas rapidly decreases near a virial radius, and the gas returns to a galactic centre finally as a fountain flow. Also, the metal inflow and outflow rates sensitively depend on the halo mass and redshift. At $z=3$, the inflow rate becomes larger than the outflow one if $M_{\rm h} \gtrsim 10^{13.0}~\rm M_{\odot}$. Thus, we suggest that massive haloes cannot be efficient metal enrichment sources beyond virial radii that will be probed in future observations, e.g., studies of metal absorption lines with the Prime Focus Spectrograph on the Subaru telescope.Comment: 13 pages, 10 figures, accepted for publication in MNRA