Enlarged Symmetry Research Articles

Group Theory on Quasisymmetry and Protected Near Degeneracy.

In solid state systems, group representation theory is powerful in characterizing the behavior of quasiparticles, notably the energy degeneracy. While conventional group theory is effective in answering yes-or-no questions related to symmetry breaking, its application to determining the magnitude of energy splitting resulting from symmetry lowering is limited. Here, we propose a theory on quasisymmetry and near degeneracy, thereby expanding the applicability of group theory to address questions regarding large-or-small energy splitting. Defined within the degenerate subspace of an unperturbed Hamiltonian, quasisymmetries form an enlarged symmetry group eliminating the first-order splitting. This framework ensures that the magnitude of splitting arises as a second-order effect of symmetry-lowering perturbations, such as external fields and spin-orbit coupling. We systematically tabulate the quasisymmetry groups within 32 crystallographic point groups and find all the possible unitary quasisymmetry group structures regarding double degeneracy. Applying our theory to the realistic material AgLa, we predict a "quasi-Dirac semimetal" phase characterized by two tiny-gap band anticrossings.

Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator

We propose bi-critical and tri-critical theories between chiral spin liquid (CSL), topological superconductor (SC) and charge density wave (CDW) ordered Chern insulator with Chern number C=2C=2 on square, triangular and Kagome lattices. The three CDW order parameters form a manifold of S^2S2 or S^1S1 depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge 2e2e and its condensation leads to a topological superconductor. The CDW-SC transitions are in the same universality classes as the celebrated deconfined quantum critical points (DQCP) between Neel order and valence bond solid order on square lattice. Both SC and CDW order can be accessed from the CSL phase through a continuous phase transition. At the CSL-SC transition, there is still CDW order fluctuations although CDW is absent in both sides. We propose three different theories for the CSL-SC transition (and CSL to easy-plane CDW transition): a U(1)U(1) theory with two bosons, a U(1)U(1) theory with two Dirac fermions, and an SU(2)SU(2) theory with two bosons. Our construction offers a derivation of the duality between these three theories as well as a promising physical realization. The SU(2)SU(2) theory offers a unified framework for a series of fixed points with explicit SO(5), O(4)SO(5),O(4) or SO(3)× O(2)SO(3)×O(2) symmetry. There is also a transparent duality transformation mapping SC order to easy-plane CDW order. The CSL-SC-CDW tri-critical points are invariant under this duality mapping and have an enlarged SO(5)SO(5) or O(4)O(4) symmetry. The DQCPs between CDW and SC inherit the enlarged symmetry, emergent anomaly, and self-duality from the tri-critical point. Our analysis unifies the well-studied DQCP between symmetry breaking phases into a larger framework where they are proximate to a topologically ordered phase. Experimentally the theory demonstrates the possibility of a rich phase diagram and criticality through closing the Mott gap of a quantum spin liquid with projective symmetry group.

Unification of Gravity and Internal Interactions

AbstractIn the gauge theoretic approach of gravity, general relativity is described by gauging the symmetry of the tangent manifold in four dimensions. Usually the dimension of the tangent space is considered to be equal to the dimension of the curved manifold. However, the tangent group of a manifold of dimension d is not necessarily . It has been suggested earlier that by gauging an enlarged symmetry of the tangent space in four dimensions one could unify gravity with internal interactions. Here, such a unified model is considered by gauging the as the extended Lorentz group overcoming in this way some difficulties of the previous attempts of similar unification and eventually obtained the GUT, supplemented by an global symmetry.

On the electromagnetic symmetry producing fields charges at four bosons association

Physics would like to know what electric charge is. As a matter property it generates EM fields, coupling constant,conserved current. Nevertheless Maxwell is uncomplete. It requires to be extended. An approach is supported byelectric charge transfer phenomenology. Consider on three flavours charges {+, 0, −} transmission.A generic electric charge is defined by the triad {+, 0, −}. It provides an exchange charge physics through thequadruplet {Aμ, Uμ, V ± μ }. An electromagnetic symmetry is constituted. It associates the four vectorial bosons. TheEM completeness of particles carrying three electric charges is found. A four photons EM is derived. It includes, Aμ asthe usual photon, Uμ massive photon, V±μ massive charged photons. A new electromagnetic physics is expressed through an enlarged abelian symmetry, Uq(1). Maxwell relationshipsbetween charge and fields are extended. Fields charges are more primitive than electric charge. Noether theoremimproves the attributes on electric charge conservation, symmetry equation and constraint. The symmetry equationwhich govern the electric charge dynamics shows a charge behaviour beyond matter, as fields flux. EM interaction isextended from fine structure constant to modulated and neutral charges.The four bosons electromagnetism introduces a non-univoque electromagnetic symmetry. A pluriformity of EM modelsis performed under similar abelian group, Uq(1). Opportunities for different EM models are constituted preservingcharge conservation law and sharing a common Lagrangian. Physical varieties on Noether theorem, fields strengths,Lagrangian coefficients, equations of motion, fields charges are expressed. Electric charge is englobed by fields charges.The simplest four bosons model is selected. That one which fields strengths are gauge invariants. Propitiatingmeasurable granular and collective fields strenghts. Four kinds of charges are expressed through equations of motion.Electric, modulate, neutral and Bianchi. Allowing to include new EM sectors. Extend Maxwell for nonintegers charges,nonlinearity, neutral EM, spintronics, weak interactions, photonics. A new EM energy emerges.

Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals

Linearly dispersing Rarita-Schwinger-Weyl (RSW) fermions featuring two Fermi velocities are the key constituents of itinerant spin-3/2 quantum materials. When doped, RSW metals sustain two Fermi surfaces (FSs), around which one fully gapped $s$ wave and five mixed-parity local pairings can take place. The intraband components of four mixed-parity pairings support point nodes at the poles of two FSs, only around which long-lived quasiparticles live. For weak (strong) pairing amplitudes ($\mathrm{\ensuremath{\Delta}}$), gapless north and south poles belonging to the same (different) FS(s) get connected by polar hairs, one-dimensional line nodes occupying the region between two FSs. The remaining one, by contrast, supports four nodal rings in between two FSs, symmetrically placed about their equators, but only when $\mathrm{\ensuremath{\Delta}}$ is small. For large $\mathrm{\ensuremath{\Delta}}$, this paired state becomes fully gapped. The transition temperature and pairing amplitudes follow the BCS scaling. We explicitly showcase these outcomes for a rotationally symmetric RSW metal and contrast our findings when the system possesses an enlarged Lorentz symmetry and with those in spin-3/2 Luttinger materials.

Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes

We study a mechanism whereby quantum information present in the initial state of a quantum many-body system can be protected for arbitrary times due to a combination of symmetry and spatial locality. Remarkably, the mechanism is sufficiently generic that the dynamics can be fully ergodic upon resolving the protecting symmetry and fixing the encoded quantum state, resulting in a quantum memory that persists up to infinite temperature. After exemplifying the mechanism in a strongly nonintegrable two-dimensional (2D) spin model inspired by the surface code, we find it has a natural interpretation in the language of noiseless subsystems and stabilizer subsystem codes. This interpretation yields a number of further examples, including a nonintegrable Hamiltonian with quantum memory based on the Bacon-Shor code. The lifetime of the encoded quantum information in these models is infinite provided that the dynamics respect the stabilizer symmetry of the underlying subsystem code. In the presence of symmetry-violating perturbations, we make contact with previous work leveraging the concept of prethermalization to show that the encoded quantum information can acquire a parametrically long lifetime under dynamics with an enlarged continuous symmetry group. The prethermalization mechanism hinges on the application of external fields that are much larger than the perturbations themselves. We identify conditions on the underlying subsystem code that enable such a prethermal enhancement of the memory lifetime.3 MoreReceived 28 October 2021Revised 15 February 2022Accepted 1 April 2022DOI:https://doi.org/10.1103/PRXQuantum.3.020330Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum memoriesQuantum InformationCondensed Matter, Materials & Applied Physics

Symmetry enriched phases of quantum circuits

Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a broader perspective, these circuits generate a novel ensemble of quantum many-body states at their output. In this paper, we characterize this ensemble and classify the phases that can be established as steady states. Symmetry plays a nonstandard role in that the physical symmetry imposed on the circuit elements does not on its own dictate the possible phases. Instead, it is extended by dynamical symmetries associated with this ensemble to form an enlarged symmetry. Thus, we predict phases that have no equilibrium counterpart and could not have been supported by the physical circuit symmetry alone. We give the following examples. First, we classify the phases of a circuit operating on qubit chains with Z2 symmetry. One striking prediction, corroborated with numerical simulation, is the existence of distinct volume-law phases in one dimension, which nonetheless support true long-range order. We furthermore argue that owing to the enlarged symmetry, this system can in principle support a topological area-law phase, protected by the combination of the circuit symmetry and a dynamical permutation symmetry. Second, we consider a Gaussian fermionic circuit that only conserves fermion parity. Here the enlarged symmetry gives rise to a U(1) critical phase at moderate measurement rates and a Kosterlitz–Thouless transition to area-law phases. We comment on the interpretation of the different phases in terms of the capacity to encode quantum information. We discuss close analogies to the theory of spin glasses pioneered by Edwards and Anderson as well as crucial differences that stem from the quantum nature of the circuit ensemble.

Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for mathcal{N} = 1 and mathcal{N} = 2 pure AdS supergravity in D = 4 for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the mathcal{N} = 2 case, it follows that this amounts to the introduction of a θ-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the θ-ambiguity of gauge theory.We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with OSp( mathcal{N} |2) gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D’Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravity.

Twisted bilayer graphene. III. Interacting Hamiltonian and exact symmetries

We derive the explicit Hamiltonian of twisted bilayer graphene (TBG) with Coulomb interaction projected into the flat bands, and study the symmetries of the Hamiltonian. First, we show that all projected TBG Hamiltonians can be written as Positive Semidefinite Hamiltonian, the first example of which was found in [PRL 122, 246401]. We then prove that the interacting TBG Hamiltonian exhibits an exact U(4) symmetry in the exactly flat band (nonchiral-flat) limit. We further define, besides a first chiral limit where the AA stacking hopping is zero, a new second chiral limit where the AB/BA stacking hopping is zero. In the first chiral-flat limit (or second chiral-flat limit) with exactly flat bands, the TBG is enhanced to have an exact U(4)$\times$U(4) symmetry, whose generators are different between the two chiral limits. While in the first chiral limit and in the non-chiral case these symmetries have been found in [PRX 10, 031034] for the $8$ lowest bands, we here prove that they are valid for projection into any $8 n_\text{max}$ particle-hole symmetric TBG bands, with $n_\text{max}>1$ being the practical case for small twist angles $<1^\circ$. Furthermore, in the first or second chiral-nonflat limit without flat bands, an exact U(4) symmetry still remains. We also elucidate the link between the U(4) symmetry presented here and the similar but different U(4) of [PRL 122, 246401]. Furthermore, we show that our projected Hamiltonian can be viewed as the normal-ordered Coulomb interaction plus a Hartree-Fock term from passive bands, and exhibits a many-body particle-hole symmetry which renders the physics symmetric around charge neutrality. We also provide an efficient parameterization of the interacting Hamiltonian. The existence of two chiral limits, with an enlarged symmetry suggests a possible duality of the model yet undiscovered.

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

We derive the Hamiltonian for trilayer moir\'e systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror-symmetry with respect to the middle layer. We provide a full symmetry analysis of the non-interacting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high velocity Dirac fermions, and we identify a hidden non-local symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of non-interacting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wavefunctions and derive the full many-body Hamiltonian of the system. We also provide an efficient parameterization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the $\mathrm{U} \left( 2 \right) \times \mathrm{U} \left( 2 \right)$ spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large $\mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right)$ symmetry in the chiral limit. Moreover, by identifying a new symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets* *GYU, NVM, and ZYM acknowledge the support from the RGC of Hong Kong SAR China (Grant Nos. GRF 17303019 and 17301420), the National Key Research and Development Program of China (Grant No. 2016YFA0300502), and the Strategic Priority Research Program of the Chinese Academy of

Recent experiments [Guo et al., Phys. Rev. Lett. 124 206602 (2020)] on thermodynamic properties of the frustrated layered quantum magnet SrCu2(BO3)2 — the Shastry–Sutherland material — have provided strong evidence for a low-temperature phase transition between plaquette-singlet and antiferromagnetic order as a function of pressure. Further motivated by the recently discovered unusual first-order quantum phase transition with an apparent emergent O(4) symmetry of the antiferromagnetic and plaquette-singlet order parameters in a two-dimensional “checkerboard J-Q” quantum spin model [Zhao et al., Nat. Phys. 15 678 (2019)], we here study the same model in the presence of weak inter-layer couplings. Our focus is on the evolution of the emergent symmetry as the system crosses over from two to three dimensions and the phase transition extends from strictly zero temperature in two dimensions up to finite temperature as expected in SrCu2(BO3)2. Using quantum Monte Carlo simulations, we map out the phase boundaries of the plaquette-singlet and antiferromagnetic phases, with particular focus on the triple point where these two ordered phases meet the paramagnetic phase for given strength of the inter-layer coupling. All transitions are first-order in the neighborhood of the triple point. We show that the emergent O(4) symmetry of the coexistence state breaks down clearly when the interlayer coupling becomes sufficiently large, but for a weak coupling, of the magnitude expected experimentally, the enlarged symmetry can still be observed at the triple point up to significant length scales. Thus, it is likely that the plaquette-singlet to antiferromagnetic transition in SrCu2(BO3)2 exhibits remnants of emergent O(4) symmetry, which should be observable due to additional weakly gapped Goldstone modes.

Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

We study topological phases in one-dimensional open Floquet systems driven by chiral symmetric nonunitary time evolution. We derive a procedure to calculate topological numbers from nonunitary time-evolution operators with chiral symmetry. While the procedure has been applied to open Floquet systems described by nonunitary time-evolution operators, we give the microscopic foundation and clarify its validity for the first time. We construct a model of chiral symmetric nonunitary quantum walks classified into class BDI$^\dagger$ or AIII, which is one of enlarged symmetry classes for topological phases in open systems, based on experiments of discrete-time quantum walks. Then, we confirm that the topological numbers obtained from the derived procedure give correct predictions of the emergent edge states. We also show that the model retains $\mathcal{PT}$ symmetry in certain cases and its dynamics is crucially affected by the presence or absence of $\mathcal{PT}$ symmetry.

Three-dimensional Maxwellian extended Newtonian gravity and flat limit

In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

Analogous BMS symmetry in QED and quantum anomaly in Dirac and Weyl semimetals

We show that the asymptotic infinite dimensional enlarged gauge symmetries constructed for QED are anomalous in Weyl semimetals. This symmetry is particularly important in particle physics for its analogy with the Bondi–Metzner–Sachs (BMS) symmetries in gravity, as well as for its connection with QED soft IR theorems. This leads to observable effects, because of the induction of a new current in the material, which carries a memory of the BMS symmetry precursor.

Intertwined superfluidity and density wave order in a p -orbital Bose condensate

We study a continuum model of the weakly interacting Bose gas in the presence of an external field with minima forming a triangular lattice. The second lowest band of the single-particle spectrum ($p$-band) has three minima at non-zero momenta. We consider a metastable Bose condensate at these momenta and find that, in the presence of interactions that vary slowly over the lattice spacing, the order parameter space is isomorphic to $S^{5}$. We show that the enlarged symmetry leads to the loss of topologically stable vortices, as well as two extra gapless modes with quadratic dispersion. The former feature implies that this non-Abelian condensate is a "failed superfluid" that does not undergo a Berezinskii-Kosterlitz-Thouless (BKT) transition. Order-by-disorder splitting appears suppressed, implying that signatures of the $S^5$ manifold ought to be observable at low temperatures.

Tensor O(N) model near six dimensions: Fixed points and conformal windows from four loops

In search of nontrivial field theories in high dimensions, we study further the tensor representation of the $O(N)$-symmetric ${\ensuremath{\phi}}^{4}$ field theory introduced by Herbut and Janssen [Phys. Rev. D 93, 085005 (2016)] by using four-loop perturbation theory in two cubic interaction coupling constants near six dimensions. For infinitesimal values of the parameter $\ensuremath{\epsilon}=(6\ensuremath{-}d)/2$ we find an infrared-stable fixed point with two relevant quadratic operators for $N$ within the conformal windows $1&lt;N&lt;2.653$ and $2.999&lt;N&lt;4$, and compute critical exponents at this fixed point to the order ${\ensuremath{\epsilon}}^{4}$. Taking the four-loop beta functions at their face value we determine the higher-order corrections to the edges of the above conformal windows at finite $\ensuremath{\epsilon}$, to find both intervals to shrink to zero above $\ensuremath{\epsilon}\ensuremath{\approx}0.15$. The disappearance of the conformal windows with the increase of $\ensuremath{\epsilon}$ is due to the collision of the Wilson-Fisher $\mathcal{O}(\ensuremath{\epsilon})$ infrared fixed point with the $\mathcal{O}(1)$ mixed-stable fixed point that appears at two and persists at higher loops. The latter may be understood as a Banks-Zaks type fixed point that becomes weakly coupled near the right edge of either conformal window. The consequences and issues raised by such an evolution of the flow with dimension are discussed. It is also shown both within the perturbation theory and exactly that the tensor representation at $N=3$ and right at the $\mathcal{O}(\ensuremath{\epsilon})$ infrared-stable fixed point exhibits an emergent $U(3)$ symmetry. A role of this enlarged symmetry in possible protection of the infrared fixed point at $N=3$ is noted.

Background independence in string theory

I discuss various aspects of background independence in the context of string theory, for which so far we have no manifestly background independent formulation. After reviewing the role of background independence in classical Einstein gravity, I discuss recent results implying that there is a conflict in string theory between manifest background independence and manifest duality invariance when higher-derivative corrections are included. The resolution of this conflict requires the introduction of new gauge degrees of freedom together with an enlarged gauge symmetry. This suggests more generally that a manifestly background independent and duality invariant formulation of string theory requires significantly enhanced gauge symmetries.

Phase diagram of the underdoped cuprates at high magnetic field

The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives way to a long-range charge order with increasing magnetic field; both the orders coexist in a small intermediate region. The charge order transition is strikingly insensitive to temperature, and quickly reaches a transition temperature close to the zero-field superconducting $T_c$. We argue that such a transition along with the presence of the coexisting phase cannot be described simply by a competing orders formalism. We demonstrate that for some range of parameters there is an enlarged symmetry of the strongly coupled charge and superconducting orders in the system depending on their relative masses and the coupling strength of the two orders. We establish that this sharp switch from the superconducting phase to the charge order phase can be understood in the framework of a composite SU(2) order parameter comprising the charge and superconducting orders. Finally, we illustrate that there is a possibility of the coexisting phase of the competing charge and superconducting orders only when the SU(2) symmetry between them is weakly broken due to biquadratic terms in the free energy. The relation of this sharp transition to the proximity to the pseudogap quantum critical doping is also discussed.

Generalized pure Lovelock gravity

We present a generalization of the n-dimensional (pure) Lovelock Gravity theory based on an enlarged Lorentz symmetry. In particular, we propose an alternative way to introduce a cosmological term. Interestingly, we show that the usual pure Lovelock gravity is recovered in a matter-free configuration. The five and six-dimensional cases are explicitly studied.

Universal seesaw and 0νββ in new 3331 left-right symmetric model

We consider a class of left-right symmetric model with enlarged gauge group SU(3)c×SU(3)L×SU(3)R×U(1)X without having scalar bitriplet. In the absence of scalar bitriplet, there is no Dirac mass term for fermions including usual quarks and leptons. We introduce new isosinglet vector-like fermions so that all the fermions get their masses through a universal seesaw mechanism. We extend our discussion to neutrino mass and its implications in neutrinoless double beta decay (0νββ). We show that for TeV scale SU(3)R gauge bosons, the heavy-light neutrino mixing contributes dominantly to 0νββ that can be observed at ongoing experiments. The new physics contributions arising from purely left-handed currents via exchange of keV scale right-handed neutrinos and the so called mixed helicity λ-diagram can saturate the KamLANDZen bound. We show that the right handed neutrinos in this model can have mass in the sub keV range and can be long lived compared to the age of the Universe. The contributions of these right handed neutrinos to flavour physics observables like μ→eγ and muon g−2 is also discussed. Towards the end we also comment on different possible symmetry breaking patterns of this enlarged gauge symmetry to that of the standard model.