Entanglement and fidelity signatures of quantum phase transitions in spin liquid models

Abstract

We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values $u=0$ and $\ensuremath{\infty}$. We study the variation of entanglement and fidelity measures in the ground states as a function of $u$ and specially look for signatures of quantum phase transitions at $u=0$ and $\ensuremath{\infty}$. The two different entanglement measures used are $S(i)$ (the single-site von Neumann entropy) and $S(i,j)$ (the two-body entanglement). At the quantum critical point (QCP) $u=\ensuremath{\infty}$, the entanglement measure $E$ $[=S(i),S(i,j)]$ vanishes but remains nonzero at the other QCP $u=0$. The first and second derivatives of $E$ with respect to the parameter $u$ and the entanglement length associated with $S(i,j)$ are further calculated to identify special features, if any, near the QCPs. We further determine the GS fidelity $F$ and a quantity $\text{ln}|D|$ related to the second derivative of $F$ and show that these quantities calculated for finite-sized systems are good indicators of QPTs occurring in the infinite system.