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arXiv:2603.05436

Measurement Induced Asymmetric Entanglement in a Deconfined Quantum Critical Ground State

K. G. S. H. Gunawardana

quant-phcond-mat.stat-mechSubmitted Mar 5, 2026• Announced Mar 6, 2026• 0 citations• Revised Jul 28, 2026 (v2)
v1 · Mar 5, 2026v2 · Jul 28, 2026
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Abstract

In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin $1/2$ system with next-nearest-neighbour exchange interactions($K$), which shows analogues 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 post-measurement 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 post measurement states across the phase boundary under weak measurements. Especially, the trajectory $\left(\downarrow \downarrow\right)$ describing a uniform measurement outcome given the all ancilla spins initiated in the same $\left(\downarrow \right)$ 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 evidences 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 post-measurement states.

Comments
13 pages, 10 figures

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In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin 1/21/21/2 system with next-nearest-neighbour exchange interactions(KKK), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction KcK_cKc​ and in the valance bond solid phase above KcK_cKc​. 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 post-measurement 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 post measurement states across the phase boundary under weak measurements. Especially, the trajectory (↓↓)\left(\downarrow \downarrow\right)(↓↓) describing a uniform measurement outcome given the all ancilla spins initiated in the same (↓)\left(\downarrow \right)(↓) state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when K<KcK<K_cK<Kc​ whereas it weakly decreases when K>KcK>K_cK>Kc​. We argue with numerical evidences 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 post-measurement states.
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For one-dimensional non-interacting complex fermions, we compute numerically the probability distribution of the change in the entanglement entropy (EE) after saturation, resulting from a single measurement of the occupation number by using different measurements protocols. In the thermodynamic limit, the system is in the area-law phase for any monitoring strength, however we can also study the distribution in the critical phase characterized by a logarithmic scaling of the EE with system size by considering a sufficiently weak monitoring strength. For a quantum state diffusion protocol, where the change in EE is defined between two consecutive time steps, the distribution, Gaussian for weak monitoring, gradually develops symmetric exponential tails. For strong monitoring, the core turns from Gaussian to strongly peaked at zero suggesting the dominance of quantum Zeno effect. For the quantum jump and the projective measurement protocols, we observe clear deviations from Gaussianity characterized by broader and asymmetric tails, exponential for positive values of the change, and a peak at zero, likely a precursor of Zeno effect, that increases with the system size and the monitoring strength. Intriguingly, the distribution is spatially inhomogeneous. For sites around the boundary separating the subsystems defining the EE, the distribution is close to Gaussian with a broad support while for the rest of sites has asymmetric exponential tails and a much narrower support. As the monitoring strength increases, the full distribution is controlled by the boundary sites.
A deconfined quantum critical point (DQCP) is a continuous transition between ordered phases with unrelated broken symmetries, beyond the Landau-Ginzburg-Wilson paradigm. In one dimension, such a transition between a zzz-polarized ferromagnet (zFM) and a valence-bond solid (VBS) is well established numerically in a frustrated spin-1/21/21/2 chain. Here we ask whether a superconducting quantum processor can resolve this transition and its signatures despite finite-size effects and device noise. The ground states are prepared by ancilla-projected quantum imaginary-time evolution (QITE), whose exact target states are compressed by tensor-network optimization into shallow depth quantum circuits. The hardware data distinguish the phases through their order parameters, spin and dimer correlations, structure factors, correlation ratios, and snapshot distributions. The crossing of the order parameters locates the transition, and its finite-size extrapolation lies close to the thermodynamic-limit value obtained from large-scale numerics. A noise model based on the device calibration accounts quantitatively for the reduced amplitudes measured on hardware. Our findings demonstrate that a Landau-forbidden transition between competing orders can be resolved on current quantum processors.
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The entanglement entropy (EE) of the ground state of a one-dimensional Hamiltonian at criticality has a universal logarithmic scaling with a prefactor given by the central charge ccc of the underlying (1+1)(1+1)(1+1)-dimensional conformal field theory. When the system is probed by measurements, the entanglement in the critical ground state is inevitably affected due to wave-function collapse. In this paper, we study the effect of weak measurements on the entanglement scaling in the ground state of the one-dimensional critical transverse-field Ising model. For the measurements of the spins along their transverse spin axis, we identify interesting postmeasurement states associated with spatially uniform measurement outcomes. The EE in these states still satisfies the logarithmic scaling but with an alternative prefactor given by the effective central charge ceff{c}_{\mathrm{eff}}ceff​. We derive the analytical expression of ceff{c}_{\mathrm{eff}}ceff​ as a function of the measurement strength. With both numerical simulations and analytical studies, we show that for the EE averaged over all postmeasurement states based on their Born-rule probabilities, the effective central charge is independent of the measurement strength, contrary to the usual expectation that local and nonoverlapping measurements reduce the entanglement in the system. We also examine the behavior of the average EE under (biased) forced measurements where the measurement outcomes are sampled with a predetermined probability distribution without intersite correlations. In particular, we find an optimal probability distribution that can serve as a mean-field approximation to the Born-rule probabilities and lead to the same ceff{c}_{\mathrm{eff}}ceff​ behavior. The effects of the measurements along the longitudinal spin axis and the postmeasurement correlation functions are also discussed.
We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement strength exceeds a critical value. We demonstrate this effect for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of variable strength. As opposed to projective measurements describing a restricted class of open systems, the measuring device is modeled as a continuous Gaussian probe, capturing a large class of environments. By employing data collapse and studying the enhanced fluctuations at the transition, we obtain a consistent phase boundary in the space of the measurement strength and the measurement probability, clearly demonstrating a critical value of the measurement strength below which the system is always ergodic, irrespective of the measurement probability. These findings provide guidance for quantum engineering of many-body systems by controlling their environment.