Superselection Research Articles

Search for Pauli Exclusion Principle violations with Gator at LNGS

The Pauli Exclusion Principle (PEP) appears from fundamental symmetries in quantum field theories, but its physical origin is still to be understood. High-precision experimental searches for small PEP violations permit testing key assumptions of the Standard Model with high sensitivity. We report on a dedicated measurement with Gator, a low-background, high-purity germanium detector operated at the Laboratori Nazionali del Gran Sasso, aimed at testing PEP-violating atomic transitions in lead. The experimental technique, relying on forming a new symmetry state by introducing electrons into the pre-existing electron system through a direct current, satisfies the conditions of the Messiah-Greenberg superselection rule. No PEP violation has been observed, and an upper limit on the PEP violation probability of β2/2<4.8·10-29\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta ^2/2 < 4.8 \\cdot 10^{-29}$$\\end{document} (90% CL) is set. This improves the previous constraint from a comparable measurement by more than one order of magnitude.

Boundary algebras of the Kitaev quantum double model

The recent article by Jones et al. [arXiv:2307.12552 (2023)] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev’s Toric Code and in Levin-Wen string net models, and gave a bulk boundary correspondence to describe bulk excitations in terms of the boundary net of algebras. In this article, we prove the LTO axioms for Kitaev’s Quantum Double model for a finite group G. We identify the boundary nets of algebras with fusion categorical nets associated to (Hilb(G),C[G]) or (Rep(G),CG) depending on whether the boundary cut is rough or smooth, respectively. This allows us to make connections to the work of Ogata [Ann. Henri Poincaré 25, 2353–2387 (2024)] on the type of the cone von Neumann algebras in the algebraic quantum field theory approach to topological superselection sectors. We show that the boundary algebras can also be calculated from a trivial G-symmetry protected topological phase (G-SPT), and that the gauging map preserves the boundary algebras. Finally, we compute the boundary algebras for the (3 + 1)D Quantum Double model associated to an Abelian group.

(Pseudo-)Synthetic BRST quantisation of the bosonic string and the higher quantum origin of dualities

In this article I am arguing in favour of the hypothesis that the origin of gauge and string dualities in general can be found in a higher-categorical interpretation of basic quantum mechanics. It is interesting to observe that the Galilei group has a non-trivial cohomology, while the Lorentz/Poincare group has trivial cohomology. When we constructed quantum mechanics, we noticed the non-trivial cohomology structure of the Galilei group and hence, we required for a proper quantisation procedure that would be compatible with the symmetry group of our theory, to go to a central extension of the Galilei group universal covering by co-cycle. This would be the Bargmann group. However, Nature didn’t choose this path. Instead in nature, the Galilei group is not realised, while the Lorentz group is. The fact that the Galilei group has topological obstructions leads to a central charge, the mass, and a superselection rule, required to implement the Galilei symmetry, that forbids transitions between states of different mass. The topological structure of the Lorentz group however lacks such an obstruction, and hence allows for transitions between states of different mass. The connectivity structure of the Lorentz group as opposed to that of the Galilei group can be interpreted in the sense of an ER=EPR duality for the topological space associated to group cohomology. In string theory we started with the Witt algebra, and due to similar quantisation issues, we employed the central extension by co-cycle to obtain the Virasoro algebra. This is a unique extension for orientation preserving diffeomorphisms on a circle, but there is no reason to believe that, at the high energy domain in physics where this would apply, we do not have a totally different structure altogether and the degrees of freedom present there would require something vastly more general and global.

The Double Semion State in Infinite Volume

AbstractWe describe in a simple setting how to extract a braided tensor category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding to abelian anyons. We extract from this category its fusion ring as well as its F and R-symbols. We then construct the double semion state in infinite volume and extract the braided tensor category describing its semion, anti-semion, and bound state excitations. We verify that this category is equivalent to the representation category of the twisted quantum double $$\mathcal {D}^{\phi }(\mathbb {Z}_2)$$ D ϕ ( Z 2 ) .

Entanglement entropy and the boundary action of edge modes

We consider an antisymmetric gauge field in the Minkowski space of d-dimension and decompose it in terms of the antisymmetric tensor harmonics and fix the gauge. The Gauss law implies that the normal component of the field strength on the spherical entangling surface will label the superselection sectors. From the two-point function of the field strength on the sphere, we evaluate the logarithmic divergent term of the entanglement entropy of edge modes of p-form field. We observe that the logarithmic divergent term in entanglement entropy of edge modes coincides with the edge partition function of co-exact p-form on the sphere when expressed in terms of the Harish-Chandra characters. We also develop a boundary path integral of the antisymmetric p-form gauge field. From the boundary path integral, we show that the edge mode partition function corresponds to the co-exact (p − 1)-forms on the boundary. This boundary path integral agrees with the direct evaluation of the entanglement entropy of edge modes extracted from the two-point function of the normal component of the field strength on the entangling surface.

Does Quantum Mechanics Require "Conspiracy"?

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems "conspiratorial", in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell's theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis.

Superselection-resolved entanglement in lattice gauge theories: a tensor network approach

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.

Null Hamiltonian Yang–Mills theory: Soft Symmetries and Memory as Superselection

AbstractSoft symmetries for Yang–Mills theory are shown to correspond to the residual Hamiltonian action of the gauge group on the Ashtekar–Streubel phase space, which is the result of a partial symplectic reduction. The associated momentum map is the electromagnetic memory in the Abelian theory, or a nonlinear, gauge-equivariant, generalisation thereof in the non-Abelian case. This result follows from an application of Hamiltonian reduction by stages, enabled by the existence of a natural normal subgroup of the gauge group on a null codimension-1 submanifold with boundaries. The first stage is coisotropic reduction of the Gauss constraint, and it yields a symplectic extension of the Ashtekar–Streubel phase space (up to a covering). Hamiltonian reduction of the residual gauge action leads to the fully reduced phase space of the theory. This is a Poisson manifold, whose symplectic leaves, called superselection sectors, are labelled by the (gauge classes of the generalised) electric flux across the boundary. In this framework, the Ashtekar–Streubel phase space arises as an intermediate reduction stage that enforces the superselection of the electric flux at only one of the two boundary components. These results provide a natural, purely Hamiltonian, explanation of the existence of soft symmetries as a byproduct of partial symplectic reduction, as well as a motivation for the expected decomposition of the quantum Hilbert space of states into irreducible representations labelled by the Casimirs of the Poisson structure on the reduced phase space.

Mode entanglement in fermionic and bosonic Harmonium

Mode entanglement in many-body quantum systems is an active area of research. It provides crucial insight into the suitability of many-body systems for quantum information processing tasks. Local super-selection rules must be taken into account when assessing the amount of physically accessible entanglement. This requires amending well-established entanglement measures by incorporating local parity and local particle number constraints. In this paper, we report on mode entanglement present in the analytically solvable system of N-Harmonium. To the knowledge of the authors, this is the first analytic study of the physically accessible mode and mode-mode entanglement of an interacting many-body system in a continuous state space. We find that super-selection rules dramatically reduce the amount of physically accessible entanglement, which vanishes entirely in some cases. Our results strongly suggest the need to re-evaluate intra and inter-mode entanglement in other fermionic and bosonic systems.

VIP-2 with modulated current: pathfinder for enhanced Pauli exclusion principle violation studies

Fermions are subject to the Pauli Exclusion Principle (PEP), which is grounded on the spin-statistics theorem and, hence, related to the very same structure of the underlying symmetries. The VIP-2 (VIolation of Pauli exclusion principle - 2) experiment has been performing extreme sensitivity tests of the PEP, up to its current and final configuration, exploiting several experimental setups designed to study different theoretical models of PEP violation, looking for a faint signal of physics Beyond the Standard Model.A current is introduced in the copper target to bring new electrons into the system and, hence, fulfill the requirements of the Messiah-Greenberg Super-Selection rule. The searched spin-statistics violating signal corresponds to X-rays emitted when the new electrons perform atomic transitions to the already filled fundamental level of copper. This work analyzes the set of the VIP-2 data corresponding to a test run of 68 days in a current modulated regime alternating no current with current data-taking in short periods (50 s each), instead the usual alternating months-long data-taking of each of these two phases. We propose an analysis method to improve the experiment’s sensitivity: a spectral analysis constraint with the Discrete Fourier Transformation of the data. Compared to the spectrum-only analysis, about a factor of 1.5 of improvement to the limit for the probability of PEP violation for electrons was obtained.

Andreev Hidden Spinor Coordinates: Standard Model, Gravity and 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He

This paper is prepared for a special memorial issue of J. Low Temp. Phys. dedicated to the Memory of Alexander Andreev. I discuss his ideas devoted to the fundamental problem in modern physics—the origin and validity of the superselection rule, which forbids the superposition of a fermion and a boson state. Andreev suggested extra spin degrees of freedom, due to which the 2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\pi$$\\end{document} rotation does not change the sign of the fermionic wave function, and as a result the fermion-boson transmutation becomes possible. Although his approach looks somewhat contradictory from the point of view of the present physics, in principle his ideas can be realized on the more fundamental trans-Planckian level leading to new physics. Different scenarios of the extension of the internal spinor space are considered.

Algebraic Model of Non-Abelian Superselection Rules Considering Conjugate Endomorphism

Algebraic Model of Non-Abelian Superselection Rules Considering Conjugate Endomorphism

Weak equivalence principle violation for mixed scalar particles

We investigate the non-relativistic limit of the Klein–Gordon equation for mixed scalar particles and show that, in this regime, one unavoidably arrives at redefining the particle’s inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for particles with definite flavor. To clearly demonstrate this feature, we adopt the Feshbach–Villars formalism for Klein–Gordon particles. Furthermore, within the same framework, we also demonstrate that, in the presence of a weak gravitational field, the mass parameter that couples to gravity (gravitational mass) does not match the effective inertial mass. This, in turn, implies a violation of the weak equivalence principle. Finally, we prove that the Bargmann’s superselection rule, which prohibits oscillating particles on the basis of the Galilean transformation, is incompatible with the non-relativistic limit of the Lorentz transformation and hence does not collide with the results obtained.

Topological correlation in anyonic states constrained by anyonic superselection rules

Topological correlation in anyonic states constrained by anyonic superselection rules

Physical entanglement between localized orbitals

The goal of the present work is to guide the development of quantum technologies in the context of fermionic systems. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This demonstrates the significance of the number-parity superselection rule and highlights the relevance of localized few-orbital subsystems for quantum information processing tasks. Then, we explore and quantify the entanglement between localized orbitals in two systems, a tight-binding model of non-interacting electrons and the hydrogen ring. For this, we apply the first closed formula of a faithful entanglement measure, derived in (arXiv:2207.03377) as an extension of the von Neumann entropy to genuinely correlated many-orbital systems. For both systems, long-distance entanglement is found at low and high densities η, whereas for medium densities, , practically only neighboring orbitals are entangled. The Coulomb interaction does not change the entanglement pattern qualitatively except for low and high densities where the entanglement increases as function of the distance between both orbitals.

Quantum Mechanics with Real Numbers: Entanglement, Superselection Rules and Gauges

We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert space followed by an imposition of—what effectively amounts to—a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach–Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlarges the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.Quanta 2023; 12: 164–170.

On one conjugate object in the symmetric tensor C*-category and the statistics of superselection sectors

In this work, a model of a symmetric tensor 𝐶*-category with conjugation is constructed for the dimension of the object 𝑑 = 3. It is proved that the constructed conjugate object of the category satisfies the conjugation equations. The classes of morphisms between objects of the modeled category are considered and studied, and the algebra of observables in the presence of such an conjugate object is introduced. As an application of the model, we consider the theory of quantum information transfer, where it is necessary to take into account the constraints associated with the superselection rules.

Knots and entanglement

We extend the entanglement bootstrap program to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions [Ann. Phys. 418, 168164 (2020), Phys. Rev. B 103, 115150 (2021)], we define a variety of superselection sectors and fusion spaces from two axioms on the ground state entanglement entropy. In particular, we identify fusion spaces associated with knots. We generalize the information convex set to a new class of regions called immersed regions, promoting various theorems to this new context. Examples from solvable models are provided; for instance, a concrete calculation of knot multiplicity shows that the knot complement of a trefoil knot can store quantum information. We define spiral maps that allow us to understand consistency relations for torus knots as well as spiral fusions of fluxes.

Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks

Towards the goal of quantum computing for lattice quantum chromodynamics, we present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel framework was previously developed for an SU(2) lattice gauge theory in $d\leq3$ spatial dimensions and its advantages for classical and quantum algorithms have thus far been demonstrated in $d=1$. The LSH approach uses gauge invariant degrees of freedoms such as loop segments, string ends, and on-site hadrons, it is free of all nonabelian gauge redundancy, and it is described by a Hamiltonian containing only local interactions. In this work, the SU(3) LSH framework is systematically derived from the reformulation of Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons, including the addition of staggered quarks. Furthermore, the superselection rules governing the LSH dynamics are identified directly from the form of the Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been numerically confirmed to agree with the completely gauge-fixed Hamiltonian, which contains long-range interactions and does not generalize to either periodic boundary conditions or to $d>1$.

Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs

We study unusual gapped topological phases where they admit \mathbb{Z}_NℤN fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by \bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2[N×∏igcd(N,pi)]2, where p_ipi’s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.