In this work we numerically study the effect of weak measurement on deconfined quantum critical point (DQCP). Particularly, we consider the ground state of a one-dimensional spin-$1/2$ system with next-nearest-neighbor exchange interactions $\left(K\right)$, which shows an analogous phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction $K_c$ and in the valance bond solid phase above $K_c$. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy, correlation length, and order parameters of leading postmeasurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the postmeasurement states across the phase boundary under weak measurements. Specifically, the trajectory $(\downarrow \downarrow )$, describing a uniform measurement outcome given all the ancilla spins initiated in the same $(\downarrow )$ state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when $K<K_c$, whereas it weakly decreases when $K>K_c$. We argue with numerical evidence that observed asymmetry in entanglement would lead to a weak first-order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement-induced effects linked to the strength of weak measurement and probability of postmeasurement states.

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• Eigenstate thermalization
• Open quantum systems & decoherence
• Quantum coherence & coherence measures
• Quantum computation
• Quantum correlations in quantum information
• Quantum phase transitions
• Quantum simulation