Yao-Tai Kang, Department of Physics, National Tsing Hua University

We study the driven critical dynamics of the quantum link model, whose Hamiltonian describes the one-dimensional $U(1)$ lattice gauge theory. We find that combined topological defects emerge after the quench and they consist of both gauge field and matter field excitations. Furthermore, the ratio of gauge field and matter field excitation is 1/2 due to the constraint of the Gauss’ law. We show that the scaling of these combined topological defects satisfies the usual Kibble-Zurek mechanism. We verify that both the electric flux and the entanglement entropy satisfy the finite-time scaling theory in the whole driven process. Possible experimental realizations are discussed.

### Unitary Group Adapted selected CI

Vijay Chilkuri, Max Planck Institute

### Tensor network renormalization study on boundary CFT underlying classical spin models

Shumpei Iino, ISSP, University of Tokyo

Tensor network renormalization (TNR) [1] is one of the most efficient tensor renormalization group [2] algorithms, which is able to eliminate the short correlated loop and yield the correct fixed point tensor even at criticality. We implement the extended TNR algorithm so as to be applicable for the system with open boundaries, and investigate the surface critical behavior and the emergent conformal invariance. We successfully compute the boundary conformal spectrum for various classical spin models on a lattice, all of which are completely consistent with the results from the underlying boundary CFT [3].

[1] G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015). [2] M. Levin and C. P. Nave, Phys. Rev. Lett. 99, 120601 (2007). [3] S. Iino, S. Morita, and N. Kawashima, in preparation.

### Phase diagram of the SU(2)xSU(2)-invariant Penson-Kolb-Hubbard model

Roman Rausch, Department of Physics, Kyoto University

Using the variational uniform matrix product state (VUMPS) technique, we investigate the Hubbard model with a nearest-neighbor density-density (extended) term as well as a pair-hopping (Penson-Kolb) term $V$; at a point where the charge-SU(2) pseudospin symmetry is preserved. Strong positive $V$ leads to a phase where s-wave superconductivity is mixed with a charge-density wave (CDW), while strong negative $V$ leads to a phase where $\eta$-wave superconductivity is mixed with phase separation (PS). It is shown that there are also two intervening phases: For negative $V$, we find an intervening partially polarized pseudospin-ferromagnet. For positive $V$, there is a dimerized bond order wave phase (BOW) which is much broader and extends to much larger interactions than in the charge-SU(2) broken extended Hubbard model. Apart from standard techniques, we also apply machine learning to confirm its phase boundaries.

### Self-learning Monte Carlo simulation in the semiclassical site-diluted double-exchange model

Hidehiko Kohshiro, ISSP, University of Tokyo

The self-learning Monte Carlo (SLMC) method is a speed-up algorithm for Markov chain Monte Carlo simulation which employs an effective model trained to generate a Boltzmann weight similar to one of the original model[1]. SLMC method has not been applied to inhomogeneous systems. We applied SLMC method to the site-diluted the semiclassical double exchange model, where itinerant many-body electron system coupled to localized classical spins to investigate the efficiency of SLMC for disordered systems[3]. As a result of training, we observed RKKY-like exchange coupling, which oscillates with a distance between localized spins consistent with previous work [2].

[1]J. Liu et al., PRB 95, 041101(R) (2017). [2]J. Liu et al., PRB 95, 241104(R) (2017). [3]H. Kohshiro and Y. Nagai, in preparation.

### Numerical strong-disorder renormalization group for two-dimensional random quantum spin systems

Kouichi Seki, Department of Physics, Niigata University

Recently, two-dimensional (2D) frustrated quantum spin systems with random interactions attract much interest, where the randomness and frustration effects may cooperatively induce exotic spin-liquid-like behaviors[1]. However, the exact diagonalization (ED) results in the previous studies are not sufficient to conclude precise properties of such exotic behaviors. The main purpose of our study is to develop a numerical renormalization group approach that efficiently works for the 2D random quantum spin systems, on the basis of the strong-disorder renormalization groups (SDRGs)[2,3], which actually succeeded in extracting the random singlet ground state of 1D random quantum spin systems. We reformulate an SDRG algorithm for 2D random quantum spin systems and then evaluate its numerical accuracy with precise comparisons with ED results up to 24 spins. We then find that that the numerical accuracy is significantly affected by definitions of energy scale cutoffs used in renormalizing two block spins. In our presentation, we explain the physical roles of the energy scale cutoffs and then present benchmark results of our numerical SDRG for S = 1/2 triangular lattice Heisenberg antiferromagnets with box-type random exchange couplings.

[1] K. Watanabe, H. Kawamura, H. Nakano, T. Sakai, J. Phys. Soc. Jpn. 83, 034714 (2014). [2] S.-k. Ma, C. Dasgupta, and C.-k. Hu, Phys. Rev. Lett. 43, 1434 (1979). [3] T. Hikihara, A. Furusaki, and M. Sigrist, Phys. Rev. B 60, 12116 (1999).

### Direct numerical observation of Bose-Einstein condensation of deconfined spinons

Adam Iaizzi, Department of Physics, National Taiwan University

We study a 2D S=1/2 quantum antiferromagnet (the J-Q model) in the presence of an external magnetic field using quantum Monte Carlo methods. The J-Q model combines the standard Heisenberg exchange (J) with a four-spin interaction (Q) that drives a quantum phase transition from the O(3) Néel state to the valence-bond solid (a nonmagnetic state breaking Z4 lattice symmetry). This transition is believed to be an example of deconfined quantum criticality, where the critical point is described by exotic fractionalized excitations called spinons (S=1/2 bosons) [1]. We present direct evidence for the presence of these fractionalized excitations. Using a magnetic field we induce a finite ground-state density of magnetic excitations at the critical point and measure energy as a function of field and temperature. Expanding on previous work [2], we include an extra U(1) gauge field in our analysis, resulting in new predictions for the behavior of both a BEC and gas of deconfined spinons. We compare these predictions to numerical results. At low temperatures, we find behavior consistent with a Bose-Einstein condensate of deconfined spinons. At higher temperatures we find an anomalous temperature dependence that can only be explained by a gas of deconfined spinons. Our findings are also summarized in our preprint [3]. [1] H Shao, W Guo & AW Sandvik, Science 352, 213 (2016) [2] HD Scammell & OP Sushkov, Phys. Rev. Lett. 114 055702 (2015) [3] A Iaizzi, HD Scammell, OP Sushkov & AW Sandvik arXiv:1909.01594 (under review)

### Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice

Jozef Genzor, Department of Physics, National Taiwan University

The current study is an extension of our earlier study of the phase transition phenomena on a fractal lattice. Whereas the before-studied fractal lattice was embedded into the two-dimensional space, now, the embedding space is three dimensional. It can be expected that such a change of the topology would have a rather significant influence on the character of the phase transition of the system. The Hausdorff dimension of the currently-studied fractal lattice is exactly $d^{(\text{H})} = \ln32 / \ln4 = 2.5$; thus, singular behavior of the specific heat might be expected, as such behavior is already exhibited by a regular square-lattice Ising model. Indeed, we have observed a singular behavior (divergence) at $T_{\text{c}}$ of the specific heat per site $c(T)$ obtained as a numerical derivative of the bond energy $u$ with respect to the temperature, i.~e., $c(T)=d u/ dT$. We want to emphasize that this behavior is different from one observed in the case of the 2-dimensional fractal lattice with the Hausdorf dimension $d^{(H)} = \ln 12 / \ln 4 \approx 1.792$ studied earlier, where no such divergence was found. Moreover, even though the currently studied fractal is three-dimensional, the critical exponent $\beta \approx 0.059 \approx 1/17$ is smaller than the exponent in the case of the square lattice Ising model $\beta_{\text{square}}=1/8$.

*J. Genzor, A. Gendiar, and T. Nishino, Phys. Rev. E {\bf 93} (2016) 012141.