2024/12/04 by Xiao Luo, Luo, Xiao, Y. Kuramashi +1
Earth and Planetary Sciences · Physics and Astronomy · Chemistry · #Geological and Geophysical Studies #Nonlinear Waves and Solitons #Advanced NMR Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2412.02995
We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension D\rm cut→ ∞. At the vanishing chemical potential μ=0, we investigate the von Neumann and Rényi types of entanglement entropies. The central charge is determined to be c=1.97(9) by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with μ≠ 0, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point μ\rm c and the critical exponent of the correlation length ν from the μ dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of μ. This is the first successful calculation of the dynamical critical exponent with the TRG method.