Quantum Symmetry Research Articles

Colossal room-temperature non-reciprocal Hall effect.

Non-reciprocal charge transport has gained significant attention due to its potential in exploring quantum symmetry and its promising applications. Traditionally, non-reciprocal transport has been observed in the longitudinal direction, with non-reciprocal resistance being a small fraction of the ohmic resistance. Here we report a transverse non-reciprocal transport phenomenon featuring a quadratic current-voltage characteristic and divergent non-reciprocity, termed the non-reciprocal Hall effect. This effect is observed in microscale Hall devices fabricated from platinum (Pt) deposited by a focused ion beam on silicon substrates. The transverse non-reciprocal Hall effect arises from the geometrically asymmetric scattering of textured Pt nanoparticles within the focused-ion-beam-deposited Pt structures. Notably, the non-reciprocal Hall effect generated in focused-ion-beam-deposited Pt electrodes can propagate to adjacent conductors such as Au and NbP through Hall current injection. Additionally, this pronounced non-reciprocal Hall effect facilitates broadband frequency mixing. These findings not only validate the non-reciprocal Hall effect concept but also open avenues for its application in terahertz communication, imaging and energy harvesting.

Quantum Computational Complexity and Symmetry

Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for BQP (bounded-error quantum polynomial time), QMA (quantum Merlin-Arthur), QSZK (quantum statistical zero-knowledge), QIP(2) (two-message quantum interactive proofs), QIP_EB(2) (two-message quantum interactive proofs restricted to entanglement-breaking provers), and QIP (quantum interactive proofs), thus spanning the prominent classes of the quantum interactive proof hierarchy and forging a non-trivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and QAM, while leaving it as an intriguing open question to determine whether these problems are complete for these classes.

Symmetry Restoration and Quantum Mpemba Effect in Symmetric Random Circuits.

Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to nonsymmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and Z_{2} symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.

Dilaton shifts, probability measures, and decomposition

Abstract In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. Relative shifts between universes are fixed by locality and take a universal form, reflecting underlying (noninvertible, quantum) symmetries. The first part of this paper constructs a general formula for such dilaton shifts, and discusses related computations. In the second part of this paper, we comment on the relation between decomposition and ensembles.

Strong/weak duality symmetries for Jacobi–Gordon field theory through elliptic functions

Abstract It is shown that the standard sin/sinh Gordon field theory with the strong/weak duality symmetry of its quantum S-matrix, can be formulated in terms of elliptic functions with their duality symmetries, which will correspond to the classical realization of that quantum symmetry. Specifically we show that the so called self-dual point that divides the strong and the weak coupling regimes, corresponds only to one point of a set of fixed points under the duality transformations for the elliptic functions. Furthermore, the equations of motion can be solved in exact form in terms of the inverse elliptic functions; in spontaneous symmetry breaking scenarios, these solutions show that 
kink-like solitons can decay to cusp-like solitons

Braided quantum symmetries of graph C∗-algebras

We prove the existence of a universal braided compact quantum group acting on a graph [Formula: see text]-algebra in the category of [Formula: see text]-[Formula: see text]-algebras with a twisted monoidal structure, in the spirit of the seminal work of Wang. To achieve this, we construct a braided analogue of the free unitary quantum group and study its bosonization. As a concrete example, we compute this universal braided compact quantum group for the Cuntz algebra.

Rigidity on quantum symmetry for a certain class of graph C*-algebras

Quantum symmetry of graph C*-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group (C(S1)∗C(S1)∗⋯∗C(S1)︸|E(Γ)|−times,Δ) [in short, *|E(Γ)|C(S1),Δ] always acts on a graph C*-algebra for a finite, connected, directed graph Γ in the category introduced by Joardar and Mandal, where |E(Γ)| ≔ number of edges in Γ. In this article, we show that for a certain class of graphs including Toeplitz algebra, quantum odd sphere, matrix algebra etc. the quantum symmetry of their associated graph C*-algebras remains *|E(Γ)|C(S1),Δ in the category as mentioned before. More precisely, if a finite, connected, directed graph Γ satisfies the following graph theoretic properties: (i) there does not exist any cycle of length ≥2 (ii) there exists a path of length (|V(Γ)| − 1) which consists all the vertices, where |V(Γ)| ≔ number of vertices in Γ (iii) given any two vertices (may not be distinct) there exists at most one edge joining them, then the universal object coincides with *|E(Γ)|C(S1),Δ. Furthermore, we have pointed out a few counter examples whenever the above assumptions are violated.

Nontriviality of dynamical Chern-Simons gravity and the standard model

Given the growing interest in gravitational-wave and cosmological parity-violating effects in dynamical Chern-Simons (dCS) gravity, it is crucial to investigate whether the scalar-gravitational Pontryagin term in dCS gravity persists when formulated in the context of the U(1)B−L anomaly in the standard model (SM). In particular, it has been argued that dCS gravity can be reduced to Einstein gravity after “rotating away” the gravitational-Pontryagin coupling into the phase of the Weinberg operator—analogous to the rotation of the axion zero mode into the quark mass matrix. We find that dCS gravity is nontrivial if the scalar field ϕ has significant spacetime dependence from dynamics. We provide a comprehensive consideration of the dCS classical and quantum symmetries relevant for embedding a dCS sector in the SM. We find that, because of the baryon/lepton number chiral gravitational anomaly, the scalar-Pontryagin term cannot be absorbed by a field redefinition. Assuming a minimal extension of the SM, we also find that a coupling of the dCS scalar with right-handed neutrinos induces both the scalar-Pontryagin coupling and an axionlike phase in the dimension-five Weinberg operator. We comment on the issue of gauging the U(1)B−L, the observational effects with these two operators present for upcoming experiments, and the origin of dCS gravity in string theory. Published by the American Physical Society 2024

Learning quantum symmetries with interactive quantum-classical variational algorithms

A symmetry of a state |ψ⟩ is a unitary operator of which |ψ⟩ is an eigenvector. When |ψ⟩ is an unknown state supplied by a black-box oracle, the state’s symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum–classical learning scheme to systematically probe for symmetries of |ψ⟩ with no a priori assumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. An iteration of the learning algorithm can be implemented efficiently with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well for up to moderate system sizes.

Gauge theory on ρ-Minkowski space-time

We construct a gauge theory model on the 4-dimensional ρ-Minkowski space-time, a particular deformation of the Minkowski space-time recently considered. The corresponding star product results from a combination of Weyl quantization map and properties of the convolution algebra of the special Euclidean group. We use noncommutative differential calculi based on twisted derivations together with a twisted notion of noncommutative connection. The twisted derivations pertain to the Hopf algebra of ρ-deformed translations, a Hopf subalgebra of the ρ-deformed Poincaré algebra which can be viewed as defining the quantum symmetries of the ρ-Minkowski space-time. The gauge theory model is left invariant under the action of the ρ-deformed Poincaré algebra. The kinetic part of the action is found to coincide with the one of the usual (commutative) electrodynamics.

Nuclear and magnetic structure of an epitaxial La0.67Sr0.33MnO3 film using diffraction methods

We use a combination of transmission electron microscopy, X-ray and neutron diffraction, Superconducting Quantum Interference Device (SQUID) magnetometry and symmetry analysis to determine the nuclear and magnetic structure of an epitaxial La0.67Sr0.33MnO3 film, deposited on a Si substrate. The film undergoes a magnetic ordering transition at 260 K. At 300 K, in the paramagnetic phase, the manganite film has a I4/m space group. In the magnetic phase, SQUID and neutron diffraction results lead us to assign a ferromagnetic spin-order to the film, associated to magnetic moments with a slightly out-of-plane component, namely (3.5,0,0.3)μB. Symmetry analysis further shows that only the P1̄′ group is compatible with such a magnetic ordering.

Dual Optical Cycling Centers Mounted on an Organic Scaffold: New Insights from Quantum Chemistry Calculations and Symmetry Analysis.

Molecules cooled to ultracold temperatures are desirable for applications in fundamental physics and quantum information science. However, cooling polyatomic molecules with more than six atoms has not yet been achieved. Building on the idea of an optical cycling center (OCC), a moiety supporting a set of localized and isolated electronic states within a polyatomic molecule, molecules with two OCCs (bi-OCCs) may afford better cooling efficiency by doubling the photon scattering rate. By using quantum chemistry calculations, we assess the extent of the coupling of the two OCCs with each other and the molecular scaffold. We show that promising coolable bi-OCC molecules can be proposed by following chemical design principles.

Quantum smooth uncertainty principles for von Neumann bi-algebras

In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify a number of uncertainty principles on quantum symmetries, such as subfactors, fusion bialgebras, etc., studied in quantum Fourier analysis. We also obtain Wigderson–Wigderson type uncertainty principles for von Neumann bi-algebras. Moreover, we give a complete answer to a conjecture proposed by A. Wigderson and Y. Wigderson.

Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras

AbstractWe find a finite free resolution of the counit of the free unitary quantum groups of van Daele and Wang and, more generally, Bichon's universal cosovereign Hopf algebras with a generic parameter matrix. This allows us to compute Hochschild cohomology with one‐dimensional coefficients for all these Hopf algebras. In fact, the resolutions can be endowed with a Yetter–Drinfeld structure. General results of Bichon then allow us to compute also the corresponding bialgebra cohomologies. Finding the resolution rests on two pillars. We take as a starting point the resolution for the free orthogonal quantum group presented by Collins, Härtel, and Thom or its algebraic generalization to quantum symmetry groups of bilinear forms due to Bichon. Then, we make use of the fact that the free unitary quantum groups and some of its non‐Kac versions can be realized as a glued free product of a (non‐Kac) free orthogonal quantum group with , the finite group of order 2. To obtain the resolution also for more general universal cosovereign Hopf algebras, we extend Gromada's proof from compact quantum groups to the framework of matrix Hopf algebras. As a by‐product of this approach, we also obtain a projective resolution for the freely modified bistochastic quantum groups. Only a special subclass of free unitary quantum groups and universal cosovereign Hopf algebras decompose as a glued free product in the described way. In order to verify that the sequence we found is a free resolution in general (as long as the parameter matrix is generic, two conditions which are automatically fulfilled in the free unitary quantum group case), we use the theory of Hopf bi‐Galois objects and Bichon's results on monoidal equivalences between the categories of Yetter–Drinfeld modules over universal cosovereign Hopf algebras for different parameter matrices.

Woldemar Voigt’s Alliance of Finite Reality with Infinite Fantasy

This article tries to explain why we should ally the cerebral and asymmetrical finiteness spared in autism with the cerebellar and symmetrical infinity impaired in it to avoid global warming, a super-wicked problem. Woldemar Voigt implied the alliance of detectible finiteness and lying infinity in 1887 at the University of Göttingen through the transformations of his “Shining Sphere,” or Riemann Sphere. Since they cannot lie, autistics cannot face problems, rooted in the maybe of dreaming and fantasy. The author posits that our problem is ignoring the alliance of classical asymmetry and quantum symmetry in our brainstem, Stonehenge’s builders, artless discourse, and nature’s nature. The author posits that recalling nature’s roots will save about eight billion nonautistic liars (rooted in the “tree of knowledge”) from a fate worse than Lisbon’s Earthquake in 1755. The ruin of life on Earth can wane by willfully grasping the union of vertical and finite asymmetry with horizontal and infinite symmetry in the “tree of life.” Asymmetrical finiteness (e.g., from front to back in a dog tick) hugs symmetrical infinity in living beings (e.g, the legs and eyes of a dog tick) as relativity hugs quantum physics; and Descartes’ cosines hug Euler’s sines in a complex plane.

Sensing applications of graphitic carbon nitride (g-C3N4) for sensing SO2 and SO3 – A DFT study

Gas sensors are instruments that detects and monitors the presence of harmful and toxic gases in the atmosphere. They are an essential tool for maintaining environmental health, air quality, and safety, and their invention has prompted an extensive research and advancement in the field of gas detection. The sensing and adsorption behaviour of graphitic carbon nitride are analyzed to detect noxious gases SO2 and SO3 using density functional theory. Upon absorption of SO2 and SO3 analytes on the surface of the carbon nitride (C6N8), moderate physiorption for the SO2 analyte (−37.11 kJ mol−1), and high chemisorption for SO3 analyte (−67.90 kJ mol−1) are observed. The interaction energies depict weak van der Waals forces that is further demonstrated by the noncovalent interaction index (NCI), symmetry perturbation theory (SAPT0) and quantum theory of atoms in molecules (QTAIM) analysis. Using the natural bond orbital analysis, UV–Vis analysis, electron localization function, molecular electrostatic potential, and density of state (DOS) analysis, the electronic properties of complexes were analyzed to determine the significant impacts of the adsorption of these analytes (SO2 and SO3) on the carbon nitride C6N8. Natural bond orbital analysis revealed that charge migration occurs from the carbon nitride C6N8 surface towards the analytes (SO2 and SO3) during complex formation that are −0.032 and −0.189 e−, for SO2@C6N8 and SO3@C6N8 complexes. The analytes (SO2 and SO3) behave as electrophiles and the carbon nitride C6N8 surface serves as a nucleophilic attack in both complexes. The chemical reactivity of both complexes was shown by the development of new excited states in the PDOS spectrum. At 300 K, the recovery period was calculated by applying the transition state theory to analyze the reusability of the carbon nitride C6N8 surface. Our finding provides a theoretical foundation for the possible use of carbon nitride C6N8 surface for gas sensors targeting significant air pollutants such as SO2 and SO3 in the environment.

Mixed quantum/classical theory (MQCT) approach to the dynamics of molecule-molecule collisions in complex systems.

We developed a general theoretical approach and a user-ready computer code that permit study of the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture of classical and quantum mechanics. The internal ro-vibrational motion of collision partners is treated quantum mechanically using a time-dependent Schrödinger equation that captures many quantum phenomena including state quantization and zero-point energy, propensity and selection rules for state-to-state transitions, quantum symmetry and interference phenomena. A significant numerical speed up is obtained by describing the translational motion of collision partners classically, using the Ehrenfest mean-field trajectory approach. Within this framework a family of approximate methods for collision dynamics is developed. Several benchmark studies for diatomic and triatomic molecules, such as H2O and ND3 collided with He, H2 and D2, show that the results of MQCT are in good agreement with full-quantum calculations in a broad range of energies, especially at high collision energies where they become nearly identical to the full quantum results. Numerical efficiency of the method and massive parallelism of the MQCT code permit us to embrace some of the most complicated collisional systems ever studied, such as C6H6 + He, CH3COOH + He and H2O + H2O. Application of MQCT to the collisions of chiral molecules such as CH3CHCH2O + He, and to molecule-surface collisions is also possible and will be pursued in the future.

Preface

This volume contains contributions to the XII. International Symposium on Quantum Theory and Symmetries (QTS12) was at Czech Technical University in Prague, Czech Republic, from Monday July 24 until Friday July 28, 2023.The Symposium series “Quantum Theory and Symmetries” (QTS) is a biannual meeting intended for physicists and mathematicians who are either applying symmetries to some physical model, or are studying mathematical objects that are relevant for physical applications.The first Symposium of this series was held in Goslar (Germany) in 1999, QTS-1, then it was held in Cracow (2001) QTS-2, Cincinnati (2003) QTS-3, Varna (2005) QTS-4, Valladolid (2007) QTS-5, Lexington (2009) QTS-6, Prague (2011) QTS-7, Mexico-city (2013) QTS-8, Yerevan (2015) QTS-9, Varna (2017) QTS-10, Montreal (2019) QTS-11.The Symposium QTS-12 was first planned to be in Moscow at the Moscow Institute of Physics and Technology in 2021, but was postponed by one year due to Covid-19, then it was postponed to 2023, July 24-28, and was held in Prague at the Czech Technical University (Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, CTU in Prague) QTS-12.The Symposium QTS-13 is planned for the 2nd half of July 2025 to be held in Yerevan, Armenia.The volume is organised as follows: it starts with notes in memory of H. D. Doebner. Then the invited talks at the plenary sessions and the public lecture are published followed by contributions in the parallel and poster sessions in alphabetical order.List of Editors, Advisory committee are available in this Pdf.

Analytical results for a spin–orbit coupled atom held in a non-Hermitian double well under synchronous combined modulations

We propose a simple method of synchronous combined modulations to generate the exact analytic solutions for a spin–orbit (SO) coupled ultracold atom held in a non-Hermitian double-well potential. Based on the obtained analytical solutions, we mainly study the parity-time () symmetry of this system and the system stability for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, the effect of the proportional constants between synchronous combined modulations and the SO-coupling strength on the -symmetry breaking is revealed analytically. Surprisingly, we find when the Zeeman field is present, the stable spin-flipping tunneling between two wells cannot occur in the non-Hermitian SO-coupled ultracold atomic system, but the stable spin-conserving tunneling can be performed. Under unbalanced gain and loss, the unique set of parameter conditions that can cause the system to stabilize is found. The results may provide a possibility for the exact control of -symmetry breaking and quantum spin dynamics in a non-Hermitian SO-coupled system.

Mixed permutation symmetry quantum phase transitions of critical three-level atom models

We define the concept of Mixed Symmetry Quantum Phase Transition (MSQPT), considering each permutation symmetry sector \muμ of an identical particles system, as singularities in the properties of the lowest-energy state into each \muμ when shifting a Hamiltonian control parameter \lambdaλ. A three-level Lipkin-Meshkov-Glick (LMG) model is chosen to typify our construction. Firstly, we analyze the finite number NN of particles case, proving the presence of MSQPT precursors. Then, in the thermodynamic limit N\to∞N→∞, we calculate the lowest-energy density inside each sector \muμ, augmenting the control parameter space by \muμ, and showing a phase diagram with four different quantum phases.