We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling
dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions.
Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg chain with a
single-ion anisotropy D, which has a quantum phase transition between a Haldane phase and a large-D phase. Using symmetric multiscale entanglement renormalization ansatz (MERA) tensor networks, we study the nonlocal order parameters for time-reversal and inversion symmetry. For the inversion symmetric MERA, we propose a brick-and-rope representation that gives a geometrical interpretation of inversion symmetric tensors. Finally, we study the symmetric renormalization group (RG) flow of the inversion symmetric string-order parameter, and show that entanglement renormalization with symmetric tensors produces proper behavior of the RG fixed-points.
We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional $Ltimes L times L$ cubic lattice using the graphics processing unit (GPU). By the combination of Metropolis single-spin flip, over-relaxation and parallel
-tempering methods, we simulate systems up to L=160. Performing the finite-size scaling analysis, we obtain estimates of the critical exponents for the three-dimensional XY universality class: $alpha=-0.01293(48)$ and $ u=0.67098(16)$. Our estimate for the correlation-length exponent $ u$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $ u_{rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment.
