Quantum phase transitions in a frustration-free spin chain based on modified Motzkin walks

Abstract

Area law violations for entanglement entropy in the form of a square root has recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here, we further modify the Motzkin walks using the elements of a symmetric inverse semigroup as basis states on each step of the walk. This change alters the number of paths allowed in the Motzkin walks and by introducing an appropriate term in the Hamiltonian with a tunable parameter we show that we can jump from a state that violates the area law logarithmically to a state that obeys the area law providing an example of quantum phase transition in a one-dimensional system.