This note extends the evidence framework into the nonperturbative symmetry-breaking regime of the massive Schwinger model at θ=π. Using the standard zero-mode reduction, the paper studies the transition from a symmetric potential to a broken-symmetry double-well structure and investigates how symmetry breaking changes the accessibility of quantum information. The paper shows that the phase transition is also a transition in record formation: as the two broken-symmetry states become more separated, their distinguishability through partial observations increases. The growth of the order parameter is directly connected to the birth of readable records. The work establishes a critical amplification effect: information about nearby θ-sectors becomes dramatically more accessible near and beyond the transition. The enhancement is caused by the localization crossover, where the energy bias between sectors overcomes tunneling between the two wells. The study also shows continuity with the previous Gaussian record framework in the weak-coupling limit, while revealing new non-Gaussian record behavior in the broken-symmetry regime. The central result is that symmetry breaking does not only create new phases of matter; it creates new channels through which quantum information becomes observable. The phase transition acts as an evidence amplifier. All results are obtained within the declared zero-mode reduction framework and verified with reproducibility tools. Extensions beyond this solvable reduction remain open.
This note extends the evidence framework into the nonperturbative symmetry-breaking regime of the massive Schwinger model at θ=π. Using the standard zero-mode reduction, the paper studies the transition from a symmetric potential to a broken-symmetry double-well structure and investigates how symmetry breaking changes the accessibility of quantum information. The paper shows that the phase transition is also a transition in record formation: as the two broken-symmetry states become more separated, their distinguishability through partial observations increases. The growth of the order parameter is directly connected to the birth of readable records. The work establishes a critical amplification effect: information about nearby θ-sectors becomes dramatically more accessible near and beyond the transition. The enhancement is caused by the localization crossover, where the energy bias between sectors overcomes tunneling between the two wells. The study also shows continuity with the previous Gaussian record framework in the weak-coupling limit, while revealing new non-Gaussian record behavior in the broken-symmetry regime. The central result is that symmetry breaking does not only create new phases of matter; it creates new channels through which quantum information becomes observable. The phase transition acts as an evidence amplifier. All results are obtained within the declared zero-mode reduction framework and verified with reproducibility tools. Extensions beyond this solvable reduction remain open.
This note removes the open-boundary constraint from the lattice Schwinger model and studies the periodic theory with its physical Wilson-line zero mode. The goal is to determine which features of the previous lattice results belong to the gauge theory itself and which were caused by the boundary. Using exact diagonalization of the periodic lattice model with fermions and flux degrees of freedom, the study reveals four main results. The transition is restored: the mass-gap collapse and the critical response reappear, with the mass-direction evidence developing an interior peak near the transition region. The θ-lock is recovered at zero fermion mass, with the sector energy sensitivity strongly reduced compared with the open-boundary case, while the mass-induced unlock follows the expected perturbative behavior and becomes critically enhanced near the transition. The transition-amplifier law also returns: sector evidence grows monotonically with the mass deformation, showing that the open-boundary inversion was a boundary artifact caused by pinning both sectors to a single vacuum. The central result is a record-migration law. In the massless theory, the θ-record is stored mainly in matter correlations and can be accessed through charged endpoints of spatial cuts. In the massive broken phase, the record moves into the topological flux sector: the competing vacua differ by a Wilson-loop flux, making the information invisible to purely matter-based local observers. This establishes how the location of quantum information changes across phases of an interacting gauge theory: symmetry breaking does not only create records, it determines who can access them. The results are obtained within the finite periodic lattice framework, with bounded system sizes, rotor truncation checks, and no continuum extrapolation.
This work uses the floor theorem as a quantitative probe of how information is distributed across a quantum phase transition. The system is the massive Schwinger model at θ = π, where an earlier record-susceptibility analysis located the finite-size transition. Here, neighboring ground states are analyzed through the local-unitary floor and its exact Fisher-information decomposition. Three main results are obtained. First, the floor theorem remains quantitatively valid throughout the transition. Across sixteen mass intervals, the directly measured local-unitary floor agrees with the ratio F_cl/F_Q at every point, with a maximum deviation of 0.0019. Thus the theorem functions as an accurate diagnostic even in the rapidly changing critical region. Second, the critical record is overwhelmingly coherence-borne. The population fraction of the quantum Fisher information drops to approximately 0.043 near the transition, implying that about 95.65% of the critical sensitivity is carried by eigenvector rotation rather than eigenvalue populations. Away from criticality, the information becomes progressively more population-borne, with the floor rising to approximately 0.39 by the end of the sweep. The coherence minimum does not coincide exactly with the conventional fidelity-susceptibility peak. It lies below the peak at both studied lattice sizes, with the separation decreasing as system size increases. This identifies the coherence extremum as a distinct finite-size critical locator rather than merely another representation of the susceptibility maximum. Third, the symmetry-broken order record itself is found to be almost completely local-unitary erasable. The two broken-symmetry vacua have nearly identical regional spectra, giving a unitary floor of approximately 0.014. Their distinction is therefore carried predominantly by a symmetry rotation. This does not contradict the substantial protection previously found under field-preserving channels. The same order record has different fates under different allowed channel classes: it is erasable by the broken-symmetry rotation while remaining protected when the field populations carrying the order parameter are explicitly preserved. The results provide an information-theoretic anatomy of criticality in which quantum Fisher information is separated into population and coherence components, revealing that the transition is dominated by coherence rather than population rearrangement. The analysis is limited to two lattice sizes and one coupling. The finite-size scaling of the offset between the coherence minimum and the susceptibility maximum remains open.
This work extends the record-based study of the θ = π quantum phase transition in the massive lattice Schwinger model to a third lattice size, N = 20, with ground-state Hilbert-space dimension 1,662,804. The addition of the third size allows the previously observed critical-point diagnostics to be tested as finite-size scaling quantities. Using uniform three-point parabolic interpolation across N = 12, 16, and 20, the global fidelity-susceptibility peaks move as 0.2125 → 0.2364 → 0.2485, showing a monotonic drift toward the known continuum critical mass. The coherence-minimum locator identified through the local-unitary floor also moves upward with system size while remaining below the susceptibility peak. Its separation from the peak decreases, indicating that the two independent record-based locators converge toward the same critical region from below. At N = 20, several independent diagnostics agree at sub-grid resolution: the global ground-state susceptibility, six-site and four-site regional record susceptibilities, and an alternative fidelity convention all locate the same transition region. The susceptibility peak also sharpens with increasing system size, with peak heights 1.80 → 3.04 → 4.56. No critical exponent is inferred from the available three-size dataset. The information structure of the critical record evolves with size as well. The minimum local-unitary floor increases from approximately 0.019 → 0.043 → 0.061, so the critical record remains strongly coherence-dominated at N = 20, with approximately 93.9% of its Fisher information carried by the coherence sector. Finally, the identity between the local-unitary floor and the classical-to-quantum Fisher-information ratio remains valid at Hilbert-space dimension 1.66 × 10^6 to approximately 3–6 × 10^−4. The results provide three-size finite-size scaling evidence that local and global record-based observables consistently locate the θ = π transition in the lattice Schwinger model, while also revealing how the coherence content of the critical record changes with system size. The study is limited to three finite lattice sizes and a relatively coarse mass grid. No critical exponents or infinite-volume extrapolation are claimed.
This work investigates whether a quantum phase transition can be located using record distinguishability measured only within a small subsystem. Using the massive Schwinger model at θ = π, the study defines a regional record susceptibility from the fidelity distinguishability of reduced states at neighboring fermion masses and compares it directly with the conventional global ground-state fidelity susceptibility. The principal result is an exact agreement of the critical-point locators at the tested lattice sizes. On a mass grid with spacing 0.025, the global susceptibility and the regional susceptibilities of both six-site and four-site regions peak at the same pseudo-critical mass: 0.2125 for N = 12 and 0.2375 for N = 16. The peaks sharpen with increasing lattice size, while the pseudo-critical location moves upward toward the known continuum critical value m_c/g ≈ 0.3335. A half-step refinement around the N = 16 maximum moves the estimate to 0.24375, consistent with the expected finite-size drift from below. A particularly strong locality result is that an observer holding only four sites together with the Wilson-line rotor identifies the same transition location as the full many-body state. The matter sector provides an additional test. Even after the rotor is traced out, the matter-only regional susceptibility peaks at the same pseudo-critical point. Thus, although the order record itself migrates from matter into the gauge-field zero mode across the transition, the local matter subsystem retains enough sensitivity to locate where the transition occurs. The results distinguish two different informational questions: where an order record is physically stored and where the system is maximally sensitive to a change in coupling. These need not be carried by the same degrees of freedom. This work demonstrates that, at the studied finite sizes, quantum criticality is locally record-detectable using fidelity-based reduced-state measurements. The analysis is limited to two lattice sizes and one coupling, so no continuum extrapolation or critical exponent determination is claimed.
This work synthesizes the gauge-theory branch of the quantum-record program and derives a quantitative relation between record irreversibility and Fisher information. The paper first corrects an interpretation from an earlier study of theta records. At a finite angular separation, the fraction of the record that could not be removed by local unitaries was approximately one half in both the massless and massive Schwinger models. The present tangent-space analysis shows that this apparent mass independence was a finite-angle coincidence. In the small-parameter-separation limit, the local-unitary floor is instead governed by a Fisher-information law: E = d²F_Q/8, E_spec = d²F_cl/8, and therefore E_spec/E = F_cl/F_Q, where F_Q is the quantum Fisher information and F_cl is its population, or diagonal, contribution in the eigenbasis of the reduced state. The relation is verified numerically to four decimal places at two mass values, two expansion centers, and two step sizes. The resulting floor fractions are approximately 0.639 in the massless theory and 0.495 in the massive theory. Operationally, the result states that the fraction of a parameter record that no local unitary can erase is precisely the fraction of its Fisher information encoded in eigenvalue populations rather than eigenvector rotations. The paper also consolidates eleven companion studies into a single gauge-record classification. Twenty-nine previously frozen numerical results spanning continuum field theory, interacting gauge theory, boundary conditions, theta physics, symmetry breaking, criticality, and non-Abelian center charge are audited against the general record principle. All twenty-nine are found to be mutually consistent. The resulting classification separates protected carriers—including Gauss flux, zero modes, energy, emergent conserved structures, and center charge—from erasable information classes such as arrangements, reference-frame orientation, and finite-size screening remnants. A final SU(3) diagnostic further localizes a previously observed quark–antiquark residual asymmetry. The effect appears only in the screened regime and only for one string convention, strongly indicating that it originates in the geometry of the screening cloud on the string side, although an analytic derivation remains open. The Fisher relation is demonstrated numerically in the present system rather than proven as a general operator theorem. Establishing that general theorem is the natural next theoretical step.
Whether a quantum system with a double-well effective potential undergoes spontaneous symmetry breaking depends not only on the potential landscape but also on the kinetics and the coupling with additional degrees of freedom. Here we introduce a quasi-exactly solvable model to study this problem in the context of ferroelectrics, with results that apply to a broad class of quantum phase transitions. Exploiting the analytical solutions, we provide a strict definition of the quantum paraelectric regime and identify a distinct quantum ferroelectric regime in which symmetry breaking can be realized without tunneling features. We then show that explicit symmetry breaking cannot be inferred from the order-parameter Hamiltonian alone, but requires additional couplings. This leads us to identify a regime of \emph{quantum dissipative paraelectricity}, in which observable symmetry breaking is suppressed during the evolution toward the ground state, even when the double-well structure dominates over zero-point quantum fluctuations.