Matrix Product States and Quantum Phase Transition

The study of strongly correlated systems attracts much attention from condensed matter physicists since quantum fluctuations introduce different phases with interesting physical properties. Several numerical and analytical approaches have been developed to investigate properties of low lying states. However, there is no specific framework in place to deal with the challenging problem of Quantum Phase Transition (QPT). We propose a method to detect some of QPTs based on a matrix product representation of the ground state of strongly correlated systems with local Hamiltonians. As a confirmation of our proposed method, we show that our analytical results compare favorably with numerical studies of XXZ spin-one chain with uniaxial single-ion-type anisotropy.