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 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 extends the theory of quantum records from free continuum field theory to an interacting gauge theory using the exactly solvable massless Schwinger model. The study asks whether the continuum record law survives when the relevant correlation length is not imposed by a bare mass but generated dynamically through the chiral anomaly. Using the open-boundary staggered lattice Schwinger model at fixed physical volume, external charge configurations are introduced through Gauss-law strings and records are quantified by the fidelity distinguishability of reduced edge states relative to the vacuum. Four main results are obtained. First, the gauge-theory record shows systematic convergence under lattice refinement. Although the available lattice sizes do not yet establish a high-precision continuum value, successive differences decrease and independent discretization schemes approach one another. Second, the record obeys an exponential lock law. Its distance dependence is extremely close to E ∼ exp(−2MD), where M = g/√π is the anomaly-generated Schwinger boson mass. Independent lattice sizes and source separations reproduce the predicted decay rate to within a few percent. Third, the record functional detects bosonization. The same physical record is calculated in the bosonized description as a Gaussian record of a free massive scalar field. The fermionic-to-bosonic record ratio decreases monotonically toward an order-one value under refinement, providing a direct information-theoretic bridge between the two descriptions. Fourth, a net-charge configuration produces a stable constraint record under refinement when its Gauss-law flux necessarily crosses the observer's region. The results show that the continuum record framework survives its first interacting gauge-theory test and that the exponential information-locking scale is controlled by a dynamically generated physical mass. The present study is restricted to the 1+1-dimensional massless Schwinger model, finite lattice sizes, integer external charges, and open boundaries. Higher-dimensional gauge theories and the full continuum extrapolation 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 extends the record-classification framework into a two-dimensional lattice gauge theory by studying pure Z2 gauge theory on finite tori. Using exact diagonalization in winding sectors, the work tests how quantum information is stored, distributed, and destroyed across different gauge phases. The classification survives and becomes sharper. The constraint record becomes a topological redundancy: any enclosing loop can recover the enclosed charge parity exactly at every coupling and in every phase, as a direct consequence of Gauss's law. String records appear only where confinement localizes flux into physical strings. The toric-code sector qubit forms a matter-blind record class, preserved in the topological phase but destroyed by confinement. Across the phase diagram, different records migrate or disappear, but the constraint record remains invariant. The study also identifies an important boundary case: antipodally placed charges do not produce a missing record, but an undefined local record because degenerate winding routes prevent a unique assignment. The results show that quantum records in gauge theories are determined by the underlying constraint structure and topology. Some information becomes redundantly accessible through global constraints, some becomes localized through confinement, and some survives only as nonlocal topological information. All results are obtained through exact finite-lattice calculations with documented verification checks and reproducibility data.
Quantum Darwinism explains classical objectivity through the redundant proliferation of records in an environment. This note studies that mechanism inside a gauge theory, where Gauss's law constrains which records can exist and where they can be stored. Using exact lattice Schwinger model calculations with both open and periodic boundaries, including the Wilson-line rotor, this work shows that record redundancy is determined by the relation between information and gauge constraints. Three fundamental record classes are identified. First, unscreenable charges produce perfectly redundant records: every accessible downstream region can read the same information because the constraint itself distributes the record without requiring copying dynamics. Second, screened charges produce bilocal records, with information divided between the screening cloud and the boundary-delivered image while intermediate regions remain blind. Third, symmetry-breaking order produces graded redundant records, while topological flux records represent the opposite extreme: globally distinguishable but invisible to local matter fragments. The study also reveals a constraint-induced discordant split. In the flux sector, mutual information can remain large while readable evidence is almost absent, showing that a gauge theory can contain correlations that no local fragment can convert into classical information. The central conclusion is that classical objectivity in gauge theories is not determined only by environmental interaction. It is controlled by the structure of the constraints: Gauss's law decides which records can be broadcast, localized, or hidden. All results are obtained through exact diagonalization with independent verification checks and documented numerical convergence tests.
This work tests whether the theory of quantum records survives the transition from finite lattice models to continuum quantum field theory. Using a free scalar field in 1+1 dimensions with two histories differing by a localized classical source, the record accessible to a spatial region is expressed exactly through the fidelity of equal-covariance Gaussian states. Four principal results are established. First, the continuum record functional is verified against direct truncated-Fock-space Uhlmann fidelity calculations with agreement at approximately 10^−10. Second, the lattice record converges monotonically toward the exact continuum mode-sum result under refinement from 256 to 2048 lattice sites, demonstrating that the framework is not a lattice artifact. Third, a continuum lock law is found: record evidence measured a distance L from a localized source decays as exp(−2mL), with the fitted decay rate agreeing with 2m to high precision. This identifies the finite-volume suppression observed in earlier discrete models as the lattice manifestation of a continuum correlation-length law. Fourth, the distinction between constraint records and arrangement records survives the continuum limit. As the screening length diverges, the ratio between net-charge and zero-charge rearrangement records grows approximately as 1/m², causing the constraint-class record to dominate without bound. An exploratory study of disjoint regions also finds uniformly subadditive record evidence, consistent with redundant access to a common source through continuum vacuum correlations. The results establish the first continuum realization of the record framework in an exactly controlled quantum field theory. The present analysis is restricted to a free scalar field in 1+1 dimensions and coherent mean-shift histories; interacting fields, gauge theories, massless limits, higher dimensions, and gravity remain open.
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.