We find that the measurement-induced phase transition generated by deterministic global measurements, previously observed in the integrable transverse-field Ising model (TFIM), persists in non-integrable variants of the same. To address this question, we consider the TFIM with longitudinal field and the axial next-nearest-neighbor Ising (ANNNI) model. We show that both the survival probability and the bipartite entanglement entropy consistently capture a transition between area-law and volume-law entangled phases for two distinct initial states: a product state with all spins polarized along the transverse direction and a Greenberger-Horne-Zeilinger (GHZ) state. Finite-size scaling reveals a pronounced initial state dependence: for the polarized product state, the transition point follows an inverse-square-root scaling with system size in both non-integrable models, consistent with the integrable TFIM, whereas for the GHZ initial state, it deviates from this scaling and approaches zero considerably more slowly in the non-integrable models than in the integrable TFIM. These results establish the robustness of measurement-induced transitions under deterministic measurements against integrability breaking while highlighting the crucial role of the initial state in governing their scaling behavior.
We investigate the ground-state properties and quantum critical behavior of a non-Hermitian transverse-field Ising chain subjected to longitudinal and complex transverse magnetic fields. To address this interacting many-body problem, we employ real-valued neural quantum states based on Restricted Boltzmann Machines (RBMs), optimized using Variational Monte Carlo (VMC) sampling. Spectral analysis of finite chains reveals exceptional points associated with spontaneous parity-time (PT) symmetry breaking. A real-valued RBM framework is developed to reconstruct the ground-state eigenstates of the non-Hermitian Hamiltonian. Benchmark comparisons with exact diagonalization demonstrate that the RBM approach accurately reproduces the ground-state energy, magnetization, and spin-spin correlations. Extending the analysis to larger system sizes, we identify a non-Hermitian quantum phase transition characterized by PT-symmetry breaking and the emergence of magnetic order. Our results establish real-valued neural quantum states as an efficient and scalable framework for investigating critical phenomena in interacting non-Hermitian quantum systems.
M. Ateuafack, M. Kamsap, J. Diffo et al.· 0 citations
We study post-measurement ensembles of ground states of tricritical and critical 1D quantum Ising Hamiltonians subjected, respectively, to weak energy and spin measurements without post-selection. These measurements act as relevant perturbations about the unmeasured critical ground states. Using finite-size renormalization group (RG) crossover analyses, we characterize their universal properties through the entanglement effective central charge, effective Affleck-Ludwig boundary entropy, and signatures of multifractality from moments of measurement-averaged correlation functions. In both cases, we find evidence for"measurement-dominated"or"measurement-altered"fixed points governed by the underlying Born-rule randomness. For critical Ising, we find a direct RG flow to a projective-measurement fixed point with area-law entanglement, whereas for the tricritical Ising model, we find evidence for a weak-measurement fixed point with logarithmic entanglement. These results clarify the RG-flow structure of weakly measured multicritical Ising ground states and show how intrinsic measurement-induced randomness can generate complex and rich universal long-distance scaling behavior in the post-measurement ensembles, accessible to controlled analytical RG and numerical finite-size RG crossover analyses.
Abhishek Kumar, Rushikesh A. Patil, Andreas W. W. Ludwig et al.· 2 citations
Measurement-induced phase transitions (MIPTs) in monitored quantum circuits are usually characterized by preparing steady states at different uniform measurement probabilities. Here we introduce a spatial realization of the MIPT by imposing a deterministic measurement gradient in a single monitored Clifford chain. The resulting steady state contains coexisting volume-law, critical, and area-law regions, with the point $p(x)=p_c$ acting as a spatial critical cut. By scanning entanglement observables across this profile, we show that the transition is organized by a spatial scaling form. Although this structure is analogous to finite-time scaling in temporally driven MIPT, the spatial protocol has no Kibble-Zurek dynamics. Instead, the physical bounds $0\le p\le 1$ impose a finite linear window, producing cutoff-controlled asymptotic regimes whose fitted exponents provide direct access to the correlation-length exponent $\nu$. Our results establish spatially inhomogeneous measurements as a controlled route to engineer and probe measurement-induced criticality within a single steady state.
We challenge the widespread consensus that mean-field theory fails to describe long-range open quantum systems in the presence of symmetry breaking and/or when starting from strongly correlated states (e.g., macroscopic superpositions). While recent literature relies on cumulant expansions to capture such systems, this approach rests on truncations with no clear justification. Here, we show that it is, at best, conceptually redundant in the strong long-range regime. We show that the evolution can be decomposed into, and fully reconstructed from, independent mean-field dynamics. This decomposition generates the entire hierarchy of cumulants and, as a byproduct, identifies---to our knowledge, for the first time---a regime in which cumulant expansions exactly predict low-order cumulants. We illustrate the power of our findings with two applications: we compute the moment generating function for nonequilibrium $\mathcal{Z}_2$ symmetry breaking, and construct states restoring time-translation symmetry in time crystals. In both cases, our method fully reproduces the exact many-body dynamics, which is out of reach of cumulant expansions. Our results reclaim the exactness of mean-field theory, offering a transparent framework for large-scale open quantum systems.
The tripartite quantum Rabi model couples two qubits to a bosonic mode through a collective spin-oscillator interaction, providing a simple setting for studying two-qubit entanglement. In the zero-detuning limit, the triplet part of the spectrum splits into branches with zero and maximal entanglement, while the antisymmetric singlet ladder remains exactly decoupled. Within the triplet sector, finite detuning turns the crossings between these branches into avoided crossings and redistributes this entanglement. We identify an eigenbranch whose entanglement grows from nearly zero to a nearly maximal value through such avoided-crossing mixing. The weak-coupling level ordering yields a simple analytic criterion for whether this eigenbranch has a separable weak-coupling endpoint. A three-state effective model explains how the Bell-state component becomes dominant as the coupling increases. We further use a finite-time linear ramp of the collective coupling to benchmark the final coupling and ramp time required for high Bell-state fidelity. These results show how collective spin-oscillator coupling reorganizes spectral entanglement and connects static branch structure to finite-time Bell-state preparation.
Li-Li Gao, Zi-Xuan Chen, Longlong Li et al.· 0 citations
Entanglement dynamics depend not only on how a quantum system is partitioned, but critically on how interactions across that partition are structured. For a spatial bipartition of a locally interacting system, entanglement is generated near the boundary and then propagates into the bulk. By contrast, when two extended quantum fields are coupled locally along their entire length, the interaction crosses the field-space partition everywhere, and this generates correlations throughout the system. Here, we study the entanglement dynamics between two gapless one-dimensional quantum many-body systems described by Luttinger liquid theory. The systems are initially decoupled and prepared at zero or finite temperature, after which a time-dependent tunneling interaction is activated uniformly along their length. Within a Gaussian approximation, we derive general analytical expressions for the logarithmic negativity, mutual information, and R\'enyi entropies under arbitrary coupling protocols. At zero temperature, entanglement displays an early-time power-law growth whose exponent is fixed solely by the first non-null derivative of the tunneling protocol. Once the coupling saturates, we obtain exact long-time averages of the information-theoretic quantities and characterise how the correlations scale with temperature and the final coupling strength. We also analyse how mutual information and logarithmic negativity approach the adiabatic limit for a very slow protocol with respect to intrinsic system timescale. This work extends the study of entanglement dynamics in nonequilibrium field theory to field-space partitions and mixed initial states.
L. Dupays, Taufiq Murtadho, Bi Hong Tiang et al.· 0 citations
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