Abstract
We use reduced fidelity to characterize quantum phase transitions in the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain with frustration. For the ground state and the low-lying excited states, explicit results of the reduced fidelities between the nearest-neighbor and next-nearest-neighbor spins are given in both the even-size and odd-size cases. We find the reduced fidelity is an effective tool in detecting the quantum phase transitions associated with level crossings for the finite-size systems. Interestingly, the reduced fidelity between next-nearest-neighbor spins is evidently more sensitive at the quantum phase transition points than the nearest-neighbor case. Moreover, the reduced fidelity of the low-lying excited states is a good indicator both for the first-order and infinite-order quantum phase transitions of the system.
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