Quantum Anomalies Research Articles

Hydrodynamics, anomaly inflow and bosonic effective field theory

Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the action formulation of hydrodynamics at zero temperature is reconsidered and shown to be equal to standard field-theory bosonization. Furthermore, it can be derived from a topological gauge theory in one extra dimension, which identifies the fluid variables through the anomaly inflow relations. Extending this framework to 3+1 dimensions yields an effective field theory/hydrodynamics model, capable of elucidating the mixed axial-vector and axial-gravitational anomalies of Dirac fermions. This formulation provides a platform for bosonization in higher dimensions. Moreover, the connection with 4+1 dimensional topological theories suggests some generalizations of fluid dynamics involving additional degrees of freedom.

Classification of Symmetry-Enriched Topological Quantum Spin Liquids

We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify U(1)2N chiral states and non-Abelian Ising(ν) states enriched by a p6×SO(3) or p4×SO(3) symmetry and ZN topological orders and U(1)2N×U(1)−2N topological orders enriched by a p6m×SO(3)×Z2T, p4m×SO(3)×Z2T, p6m×Z2T, or p4m×Z2T symmetry, where p6, p4, p6m, and p4m are lattice symmetries while SO(3) and Z2T are spin rotation and time-reversal symmetries, respectively. In particular, we identify symmetry-enriched topological quantum spin liquids that are not easily captured by the usual parton-mean-field approach, including examples with the familiar Z2 topological order. Published by the American Physical Society 2024

BRST cohomology is Lie algebroid cohomology

In this paper we demonstrate that the exterior algebra of an Atiyah Lie algebroid generalizes the familiar notions of the physicist's BRST complex. To reach this conclusion, we develop a general picture of Lie algebroid isomorphisms as commutative diagrams between algebroids preserving the geometric structure encoded in their brackets. We illustrate that a necessary and sufficient condition for such a diagram to define a morphism of Lie algebroid brackets is that the two algebroids possess gauge-equivalent connections. This observation indicates that the aforementioned set of Lie algebroid isomorphisms should be regarded as equivalent to the set of local diffeomorphisms and gauge transformations. Moreover, a Lie algebroid isomorphism being a chain map in the exterior algebra sense ensures that isomorphic algebroids are cohomologically equivalent. The Atiyah Lie algebroids derived from principal bundles with common base manifolds and structure groups may therefore be divided into equivalence classes of isomorphic algebroids. Each equivalence class possesses a local representative which we refer to as the trivialized Lie algebroid, and we show that the exterior algebra of the trivialized algebroid gives rise to the BRST complex. We conclude by illustrating the usefulness of Lie algebroid cohomology in computing quantum anomalies, including applications to the chiral and Lorentz-Weyl (LW) anomalies. In particular, we pay close attention to the fact that the geometric intuition afforded by the Lie algebroid (which was absent in the naive BRST complex) provides hints of a deeper picture that simultaneously geometrizes the consistent and covariant forms of the anomaly. In the algebroid construction, the difference between the consistent and covariant anomalies is simply a different choice of basis.

Loop current fluctuations and quantum critical transport

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving NN species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega>0)\sim\omega^{-2/z}σ(ω>0)∼ω−2/z, where zz is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large NN expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1N=1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega>0) \sim \omega^{-2(z-2)/z}σ(ω>0)∼ω−2(z−2)/z, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

Tilt-induced vortical response and mixed anomaly in inhomogeneous Weyl matter

We propose a nondissipative transport effect and vortical response in Weyl semimetals in the presence of spatial inhomogeneities, namely, a spatially varying tilt of the Weyl cones. We show that when the spectrum is anisotropic and tilted due to spatial lattice variations, one is confronted with generalized quantum anomalies due to the effective fields stemming from the tilt structure. In particular, we demonstrate that the position-dependent tilt parameter induces local vorticity, thus generating a chiral vortical effect even in the absence of rotation or magnetic fields. As a consequence, it couples to the electric field and thus contributes to the anomalous Hall effect.

Anomalous transport from equilibrium partition functions

We summarize recent advances in the application of the equilibrium partition function formalism for the study of the transport coefficients of relativistic fluids induced by quantum anomalies, at first and second order in the hydrodynamic expansion. We provide results for theories with Abelian and non-Abelian chiral fermions, and discuss some features of the corresponding constitutive relations.

Alternative gauged U(1)R symmetric model in light of the CDF II W -boson mass anomaly

We consider an explanation of the CDF II W boson mass anomaly by $Z\ensuremath{-}{Z}^{\ensuremath{'}}$ mixing with $U(1{)}_{R}$ gauge symmetry under which right-handed fermions are charged. It is found that $U(1{)}_{R}$ is preferred to be leptophobic to accommodate the anomaly while avoiding other experimental constraints. In such a case we require extra charged leptons to cancel quantum anomalies and the SM charged leptons get masses via interactions with the extra ones. These interactions also induce muon $g\ensuremath{-}2$ and lepton flavor violations. We discuss muon $g\ensuremath{-}2$, possible flavor constraints, neutrino mass generation via inverse seesaw mechanism, and collider physics regarding ${Z}^{\ensuremath{'}}$ production for parameter space explaining the $W$ boson mass anomaly.

Holographic Lorentz and Carroll frames

Relaxing the Bondi gauge, the solution space of three-dimensional gravity in the metric formulation has been shown to contain an additional free function that promotes the boundary metric to a Lorentz or Carroll frame, in asymptotically AdS or flat spacetimes. We pursue this analysis and show that the solution space also admits a finite symplectic structure, obtained taking advantage of the built-in ambiguities. The smoothness of the flat limit of the AdS symplectic structure selects a prescription in which the holographic anomaly appears in the boundary Lorentz symmetry, that rotates the frame. This anomaly turns out to be cohomologically equivalent to the standard holographic Weyl anomaly and survives in the flat limit, thus predicting the existence of quantum anomalies in conformal Carrollian field theories. We also revisit these results in the Chern-Simons formulation, where the prescription for the symplectic structure admitting a smooth flat limit follows from the variational principle, and we compute the charge algebra in the boundary conformal gauge.

Quantum Field Theory Anomalies in Condensed Matter Physics

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.

PACIAE 2.2.1: An updated issue of the parton and hadron cascade model PACIAE 2.2

The parton and hadron cascade model PACIAE 2.2 (cf. Yan et al. (2018) [11]) has been upgraded to the new issue of PACIAE 2.2.1 with the chiral magnetic effect (CME). The charge correlation parameter, γss and γos, which is typically used to “detect” the CME, is calculated by PACIAE 2.2.1 in Au+Au and Pb+Pb collisions, and the result is consistent with the STAR and ALICE data. As an example, PACIAE 2.2.1 model is employed to mimic the pseudorapidity distribution (dNch/dη) and transverse momentum spectra (pT) of charged particles in non-central Au+Au collisions at RHIC energy and Pb+Pb collisions at LHC energy. The chiral magnetic effect is found to partly affect the final-state basic observables in relativistic nuclear collisions. By this new issue a more realistic dynamical evolution of relativistic nuclear collisions can be depicted. Program summaryProgram Title: PACIAE version 2.2.1CPC Library link to program files:https://doi.org/10.17632/w3g68dj4d9.3Code Ocean capsule:https://codeocean.com/capsule/3695338Licensing provisions: CC By 4.0Programming language: FORTRAN 77 or GFORTRANJournal reference of previous version: Comput. Phys. Comm. 224 (2018) 417Does the new version supersede the previous version?: No.Reasons for the new version: In order that PACIAE 2.2.1 model is now able to simulate the CME-related physics and a more realistic dynamical evolution scenario in the relativistic nucleus-nucleus collisions.Summary of revisions: In PACIAE 2.2.1 model the chiral magnetic effect is introduced. The CME-induced charge separation mechanism [7] into the initial partonic states is artificially added by switching py values for a fraction f of the downward moving partons with those of the corresponding upward moving antipartons.Nature of problem: PACIAE is based on PYTHIA, where it has no any mechanisms to generate the chiral magnetic effect (CME). The CME is a novel transport phenomenon arising from the interaction between quantum anomalies and strong magnetic fields in the ultra-relativistic nuclear collisions. Charge separation is an important consequence of the CME. In order to depict the CME, the corresponding upgrade about introducing a global charge separation scheme into the initial partonic states is highly required.Solution method: The global CME-induced charge separation mechanism [7] into the initial partonic states is introduced by switching py values for a fraction f of the downward moving partons with those of the corresponding upward moving antipartons.Additional comments including restrictions and unusual features: PACIAE 2.2.1 has three versions of PACIAE 2.2.1a, 2.2.1b, and 2.2.1c. PACIAE 2.2.1a is for the elementary collision (here no upgraded from PACIAE 2.2a). PACIAE 2.2.1b and PACIAE 2.2.1c are for the nucleus-nucleus collision of A + A with input file of usu.dat. PACIAE 2.2.1b and PACIAE 2.2.1c are similar in the physical contents but are different in the topological structure [8].•Using the attached input file of usux.dat to run 1000 events for the s = 200 GeV Non Single Diffractive pp collision by PACIAE 2.2.1a takes ≈0.5 min.•Using the attached input file of usu.dat to run 10 events for the 35%-45% non-central Au+Au collisions at sNN = 200 GeV by PACIAE 2.2.1b takes ≈6 min.•Using the attached input file of usu.dat to run 10 events for the 35%-45% non-central Au+Au collisions at sNN = 200 GeV by PACIAE 2.2.1c takes ≈8 min.

Quantum Anomaly in a Dirac Fermion System with Spacetime Dependent Mass

Scientists investigate quantum anomalies in a system of Dirac fermions with spacetime dependent mass and show that the anomaly formulas can be expressed in terms of superconnections.

The anomaly that was not meant IIB

AbstractType IIB supergravity enjoys a discrete non‐Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F‐theory. Remarkably, a subtle modification of the standard 10d Chern‐Simons term cancels these anomalies, a fact which relies on thespecificfield content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green‐Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

Emergent anomalies and generalized Luttinger theorems in metals and semimetals

Whether a given material is a metal or an insulator is determined by a single parameter, the number of electrons per unit cell per spin, that is, by the filling number. When the latter is integer, the material is an insulator or a compensated semimetal. When it is fractional, the material is a metal with a Fermi surface, enclosing a volume in momentum space, determined by the fractional part of the filling -- a statement known as Luttinger's theorem. Topological semimetals provide a realization of the metallic phase, distinct from ordinary metals, as they exist at integer fillings, which normally correspond to insulators. Here, the authors develop a framework that unifies Luttinger's theorem for ordinary metals and analogous exact statements for topological semimetals. They use the language of quantum anomalies of the emergent low-energy charge conservation symmetry at each point on the Fermi surface. This framework allows one to connect topological responses in all nodal semimetals to their low-energy properties, such as the distance between the point nodes in momentum space or the area, enclosed by the nodal line.

Investigation of experimental observables in search of the chiral magnetic effect in heavy-ion collisions in the STAR experiment * *Supported by the US Department of Energy (DE-AC02-98CH10886, DE-FG02-89ER40531, DE-FG02-92ER40713, DE-FG02-88ER40424, DE-SC0012910, DE-SC0013391, DE-SC0020651), and the National Natural Science Foundation of China (12025501, 11905059, 12075085), the Strategic Priority Research Program of Chinese Academy of Science with (XDB34030200), the Fundamental Research Funds

The chiral magnetic effect (CME) is a novel transport phenomenon, arising from the interplay between quantum anomalies and strong magnetic fields in chiral systems. In high-energy nuclear collisions, the CME may survive the expansion of the quark-gluon plasma fireball and be detected in experiments. Over the past two decades, experimental searches for the CME have attracted extensive interest at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The main goal of this study is to investigate three pertinent experimental approaches: the correlator, the R correlator, and the signed balance functions. We exploit simple Monte Carlo simulations and a realistic event generator (EBE-AVFD) to verify the equivalence of the core components among these methods and to ascertain their sensitivities to the CME signal and the background contributions for the isobar collisions at the RHIC.

Exploring Anomalies by Many‐Body Correlations

The quantum anomaly is written alternatively into a form violating conservation laws or as non‐gauge invariant currents seen explicitly on the example of chiral anomaly. By reinterpreting the many‐body averaging, the connection to Pauli–Villars regularization is established which gives the anomalous term a new interpretation as arising from quantum fluctuations by many‐body correlations at short distances. This is exemplified using an effective many‐body quantum potential which realizes quantum Slater sums by classical calculations. It is shown that these quantum potentials avoid the quantum anomaly but approach the same anomalous result by many‐body correlations. Consequently, quantum anomalies might be a shortcut way of single‐particle field theory to account for many‐body effects. This conjecture is also supported since the chiral anomaly can be derived by a completely conserving quantum kinetic theory. A measure for the quality of quantum potentials is suggested to describe these quantum fluctuations in the mean energy. The derived quantum potentials might be used to describe quantum simulations in classical terms.

Gauging anomalous unitary operators

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as $C$ and $\mathit{CP}$, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

Unquantized anomalies in topological semimetals

Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may be modified qualitatively by electron-electron interactions. Here we ask the following question: what makes the topological semimetals nontrivial beyond band theory? Alternatively, can strong electron-electron interactions open a gap in topological semimetals without breaking the protecting symmetries or introducing topological order? We demonstrate that the answer is generally no, and what prevents it is their topological response, or quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses are detectable as fractional symmetry charges induced on certain gauge defects. We discuss the cases of type-I Dirac semimetals and time-reversal invariant Weyl semimetals in detail. For type-I Dirac semimetals, we also show that the anomaly vanishes, in a nontrivial manner, if the momenta of the Dirac nodes satisfy certain exceptional conditions.

SnAs: A 4K weak type-II superconductor with non-trivial band topology

Superconductors with non-trivial band topology are emerging as one of the best avenues to study quantum anomalies and experimental realization of Majorana Fermions. This article reports the successful crystal growth of superconducting SnAs, which can have topologically non-trivial states, as evidenced in DFT (Density Functional Theory) calculations, Z2 invariants and topological surface states. Here, we followed a two-step method to grow SnAs crystal. The powder XRD (X-ray Diffractometry) pattern of synthesized crystal ensures that the crystal is grown in a single phase with a NaCl type cubic structure and the EDAX (Energy Dispersive X-ray Analysis) endorses the stoichiometry of the as-grown sample. The DFT calculations performed with and without inclusion of spin-orbit coupling (SOC) show band inversion at various k symmetry points near the Fermi level. The recorded Raman spectra show two different modes, which are assigned as A1 and ETO vibrations. The ZFC (Zero-Field Cooled) & FC (Field Cooled), as well as the isothermal M − H (Magnetization vs. field) measurements, are also performed for the topological non-trivial SnAs superconductor, which eventually confirm the weak type-II superconductivity at 4K. Various other superconductivity parameters viz. kappa parameter, coherence length, and penetration depth are also calculated to probe the as-grown sample's characteristics.

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

We propose a new type of quantum liquids, dubbed Stiefel liquids, based on $2+1$ dimensional nonlinear sigma models on target space $SO(N)/SO(4)$, supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of critical quantum liquids with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and $U(1)$ Dirac spin liquid are unified as two special examples of Stiefel liquids, with $N=5$ and $N=6$, respectively. Furthermore, we conjecture that Stiefel liquids with $N>6$ are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of (conventional or parton-like) mean-field construction also means that, within the traditional approaches, it will be difficult to decide whether a non-Lagrangian state can actually emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders.

Chiral transport in curved spacetime via holography

We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic (CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses to the gravitational field similarly determined by the gravitational anomaly. The energy-momentum response is the first purely gravitational transport effect that has been related to quantum anomalies in a holographic theory.