We compute concurrence, a measure of bipartite entanglement, of the first excited state of the $1$ -D Heisenberg frustrated $J_1$ - $J_2$ spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength $\alpha=J_2/J_1\approx0.241$ , where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with $8$ sites to $16$ sites, and the value of $\alpha$ at which the change in entanglement is observed asymptotically tends to a value $\alpha_c\approx0.24116$ . We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the $1$ -D Heisenberg frustrated $J_1$ - $J_2$ spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like $2$ -D Heisenberg $J_1$ - $J_2$ model and Shastry-Sutherland model and detect quantum phase transitions.We compute concurrence, a measure of bipartite entanglement, of the first excited state of the $1$-D Heisenberg frustrated $J_1$-$J_2$ spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength $\alpha=J_2/J_1\approx0.241$, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with $8$ sites to $16$ sites, and the value of $\alpha$ at which the change in entanglement is observed asymptotically tends to a value $\alpha_c\approx0.24116$. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the $1$-D Heisenberg frustrated $J_1$-$J_2$ spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like $2$-D Heisenberg $J_1$-$J_2$ model and Shastry-Sutherland model and detect quantum phase transitions.

Sep 27, 20190 citations

Spin echo and geometric phase of a central spin coupled to a compass spin-chain

Wei Wu, Da-Wei Luo, Xu Jingbo

We investigate the Loschmidt echo of a quantum system where a central spin is symmetrically coupled to a compass spin-chain. It is found that the Loschmidt echo and its statistical distribution are able to detect the quantum criticality of the compass spin-chain at low temperature. By applying a spin flip operation to reverse the central spin's orientation, we find the controlled spin echo and its statistical distribution can effectively reveal quantum criticality at very high temperature. Moreover, we show that the geometric phase of a central spin can be used to indicate the quantum phase transition of a compass spin-chain and obeys scaling behavior in the vicinity of a quantum phase transition.We investigate the Loschmidt echo of a quantum system where a central spin is symmetrically coupled to a compass spin-chain. It is found that the Loschmidt echo and its statistical distribution are able to detect the quantum criticality of the compass spin-chain at low temperature. By applying a spin flip operation to reverse the central spin's orientation, we find the controlled spin echo and its statistical distribution can effectively reveal quantum criticality at very high temperature. Moreover, we show that the geometric phase of a central spin can be used to indicate the quantum phase transition of a compass spin-chain and obeys scaling behavior in the vicinity of a quantum phase transition.

Journal of Statistical Mechanics Theory and ExperimentJan 21, 20153 citations

We compute concurrence, a measure of bipartite entanglement, of the first excited state of the

1

-D Heisenberg frustrated

J_1

J_2

spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength

\alpha=J_2/J_1\approx0.241

, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with

8

sites to

16

sites, and the value of

\alpha

at which the change in entanglement is observed asymptotically tends to a value

\alpha_c\approx0.24116

. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the

1

-D Heisenberg frustrated

J_1

J_2

spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like

2

-D Heisenberg

J_1

J_2

model and Shastry-Sutherland model and detect quantum phase transitions.