The transition of Quantum Architectonics from a materials-centric discipline to a fundamental ontology of information-matter interaction necessitates a rigorous field-theoretic description. This study bridges that gap by promoting the Signal-Worker ontology to a continuous Gauge-Invariant Quantum Field Theory, where “Workers” are treated as fermionic matter fields and “Signals” as non-Abelian gauge bosons. We construct a $SU(2)$ invariant Lagrangian that recovers the discrete $H_{SW}$ model as a stable infrared fixed point, demonstrating that the lattice architecture of current models is a fundamental emergent reality rather than a mere approximation. The central finding of this research is the first-principles derivation of the Logical Cloning Prohibition (LCI). We demonstrate that the LCI is not merely an architectural heuristic but a symmetry-enforced conservation law—specifically, a Ward identity of the Signal gauge field. Numerical analysis reveals that the LCI scales exponentially with system size ($N$), providing robust topological protection against local decoherence. By identifying the specific anomalous terms responsible for information robustness, we provide a theoretical blueprint for the next generation of topologically protected quantum devices, validating the Signal-Worker ontology as a complete description of quantum information dynamics. Full text and updates: https://papers.qnfo.org/papers/gauge-invariant-field-theory-of-signal-worker-interactions/
The transition of Quantum Architectonics from a materials-centric discipline to a fundamental ontology of information-matter interaction necessitates a rigorous field-theoretic description. This study bridges that gap by promoting the Signal-Worker ontology to a continuous Gauge-Invariant Quantum Field Theory, where “Workers” are treated as fermionic matter fields and “Signals” as non-Abelian gauge bosons. We construct a SU(2) invariant Lagrangian that recovers the discrete HSW model as a stable infrared fixed point, demonstrating that the lattice architecture of current models is a fundamental emergent reality rather than a mere approximation. The central finding of this research is the first-principles derivation of the Logical Cloning Prohibition (LCI). We demonstrate that the LCI is not merely an architectural heuristic but a symmetry-enforced conservation law—specifically, a Ward identity of the Signal gauge field. Numerical analysis reveals that the LCI scales exponentially with system size (N), providing robust topological protection against local decoherence. By identifying the specific anomalous terms responsible for information robustness, we provide a theoretical blueprint for the next generation of topologically protected quantum devices, validating the Signal-Worker ontology as a complete description of quantum information dynamics. Full text and updates: https://papers.qnfo.org/papers/gauge-invariant-field-theory-of-signal-worker-interactions/
The current paradigm of quantum computing is increasingly constrained by a reliance on emergent quasiparticle ontologies and “epistemic patches” that obscure the underlying ab initio dynamics of quantum materials. This paper proposes a radical realignment through the “Signal-Worker” (S-W) framework, which distinguishes between fundamental fermionic workers (electrons) and bosonic signals (photons/forces). We critique the artificial truncation of fluxonium qutrit arrays and contrast them with the passive structural coherence of twistronic and Kagome lattices. Our methodology introduces the Lossless Complexity Index (LCI) as a definitive metric for “architectural intelligence,” with a generalized derivation based on the spectral entropy of the lattice. We identify a “Goldilocks zone” at LCI=1.83 where structural coherence maximizes quantum stability. Findings indicate that passive structural systems provide a 103 efficiency advantage over active flux-driven architectures, offering a robust roadmap toward high-temperature (77K) operation and a theoretical pathway to ambient-temperature computing. By demonstrating predictive divergence from standard BCS theory, we establish the S-W framework as a necessary foundation for the architectonic era of physics-instantiated computing.
Gauge theories and topological phases play a fundamental role in different areas of physics. The first ones are at the basis of the Standard Model in the field of particle physics, describing the electroweak and strong interactions through a non-Abelian gauge theory. In condensed matter and statistical physics, gauge theories arise as low-energy effective descriptions of strongly correlated phenomena, such as quantum spin liquids and quantum Hall effect. In this realm there is a strong connection with topological phases and order, as emergent gauge fermions and bosons often describe collective excitations of new exotic states of matter of spin models. The discretization on a lattice is a possible way of dealing with the strongly coupled nature of these theories, due to the fact that this formulation at finite volume provides natural regularizing cut-offs, i.e. the lattice size and spacing. This allows for the investigation of different non-perturbative properties both numerically and analytically. Despite the success of these methods, there are various aspects which remain intractable due to the sign or complex action problems, like the out of equilibrium real time evolution or the analysis of quantum chromodynamics with finite chemical potential. In this respect, quantum simulators of many-body systems to simulate high energy physics arise as promising alternatives to face these problems in the near future. They are quantum systems that can be controlled and used to simulate more complicated systems, whose properties could not be analysed with classical computational, experimental or theoretical tools. In the last decades, there has been a huge development in the fields of quantum optics and atomic physics, allowing for the realization highly precise and controllable platforms by means of trapped ions, superconducting circuits, Rydberg atoms and ultracold atoms in optical lattices. This work of Thesis is part of these fields and has different purposes, all of them connected with the study of gauge theories and topological phases. Firstly, we want to develop a reformulation of lattice gauge theories in terms of gauge invariant fields, in a way to deal solely with physical variables directly in the action. Among several possible advantages, a crucial point is that this can be particularly helpful for the construction of consistent approximation schemes, such as mean-field theories, in order to understand and capture some of the physical features of the theory and make the mean-field approximation consistent with the Elitzur theorem, stating that a local gauge symmetry can not be spontaneously broken. As a second point, we face the problem of simulating higher dimensional gauge theories with ultracold atoms. One of the challenges in more than one dimension is indeed the realization of plaquette interaction terms in the Hamiltonian of lattice gauge theories: these can be engineered through four correlated hoppings in perturbation theory, or by means of constrained hoppings in the dual formulation. In this respect, our main target is to set up an ultracold atomic platform generating the plaquette term in two dimensions using only two correlated hoppings, and protecting gauge invariance through angular momentum conservation. The last point we address in the Thesis is related to the analysis of particles moving in static background gauge potentials, i.e. when the considered gauge field has no dynamical term in the action of the system. Indeed, the dynamics of quantum particles in the presence of static gauge fields gives rise to intriguing physical phenomena. In particular, using ultracold atom setups, the realization of artificial gauge potentials can be used to investigate the physics of topological semimetals, such as Weyl or Dirac type. In the last ten years, a lot of attention has been paid to their characterization, due to the appearence of clear theoretical predictions and very well-controlled experimental techniques. We investigate here the relation between topological phase transitions and van Hove singularities, i.e. the discontinuities in the energy derivative of the density of states, in three-dimensional gapless systems. In such materials, topological phase transitions can be defined by changes of the topological invariants of the Fermi sheets, happening at specific singular points. Moreover, Fermi surface singularities result in the presence of the so-called van Hove points. We then present a general argument to relate topological phase transitions and van Hove singularities, and show observable consequences that are related to the transport properties of the system. We exemplify our argument in Weyl systems by analyzing the three-dimensional Hofstadter model for various commensurate fluxes, which offers the opportunity to consider different kinds of Weyl metals and to understand the features of their density of states.
The pursuit of macroscopic quantum coherence in strongly correlated electron systems is fundamentally limited by Planckian dissipation, a universal scattering rate that renders active-dynamic control thermodynamically untenable. This paper introduces “Quantum Architectonics,” a design paradigm that leverages passive structural intelligence to overcome this limit. We propose the “Signal-Worker” ontology to unify the physics of 2D Moiré materials and 3D bulk complex oxides (e.g., Cuprates). Central to our framework is the Lossless Complexity Index (LCI), a metric for architectural quality. We provide a first-principles derivation showing the LCI optimum is a universal constant, LCIopt=ln(2π)≈1.83, derived from the fundamental bound on quantum chaos. Our computational models, which approximate Non-Markovian dynamics, demonstrate that optimized “Phononic Scaffolds” can achieve significant coherence gains over memoryless systems. We further show that d-wave pairing symmetry in Cuprates imposes a geometric penalty on shielding efficiency compared to isotropic s-wave systems. This work establishes a rigorous, unified roadmap for engineering “owned coherence,” projecting a theoretical pathway toward stable quantum operation at 77K.
In many-body quantum systems the collective behavior of electrons can give rise to emergent phenomena that are not apparent from the underlying microscopic Hamiltonian. A particularly intriguing possibility is that the internal dynamics of a material can spontaneously generate a gauge potential A_mu^eff that couples to the electronic degrees of freedom in a manner formally identical to a conventional electromagnetic gauge field. This paper develops a theoretical framework for such self-generated gauge fields (SGGF) in quantum matter. Starting from a generic Hubbard-type model with long-range interactions, we derive an effective action for the fermions after integrating out high-energy modes. The resulting low-energy theory contains a covariant derivative D_mu = partial_mu - i A_mu^eff, where A_mu^eff emerges from the collective spin and charge fluctuations. We analyze the symmetry properties of the emergent field, show that it can acquire a mass gap or remain gapless depending on the underlying lattice geometry and interaction strength, and discuss the conditions under which it leads to novel topological responses. In particular, we identify a mechanism by which a chiral spin liquid state induces a Chern–Simons term for A_mu^eff, thereby realizing a fractional quantum Hall response without external magnetic fields. The possibility of realizing SGGF in cold atom simulators and in twisted bilayer graphene is highlighted. We conclude that the discovery of self-generated gauge fields opens a new avenue for engineering artificial fundamental interactions in solid-state platforms and for probing the interplay between topology and strong correlations.
A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian SU ( N ) and U ( N ) LGTs with dynamical matter in d + 1 D , enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for 2 + 1 D SU ( 2 ) and U ( 2 ) LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators. Published by the American Physical Society 2024
Abstract Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V, which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝ V / V 0 3 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp(V/V 0)/V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.