  We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear
sigma model at finite density using the tensor renormalization group method.
This model suffers from the sign problem, which has prevented us from
investigating the properties of the phase transition. We investigate the
properties of the phase transition by changing the chemical potential $\mu$ at
a fixed coupling of $\beta$. We determine the transition point $\mu_{\rm c}$
and the critical exponent $\nu$ from the $\mu$ 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 $\mu$.
