Low-energy Physics Research Articles

Nonperturbative regularization of ( 1+1 )-dimensional anomaly-free chiral fermions and bosons: On the equivalence of anomaly matching conditions and boundary gapping rules

A non-perturbative lattice regularization of chiral fermions and bosons with anomaly-free symmetry $G$ in 1+1D spacetime is proposed. More precisely, we ask "whether there is a local short-range quantum Hamiltonian with a finite Hilbert space for a finite system realizing onsite symmetry $G$ defined on a 1D spatial lattice, such that its low energy physics produces a 1+1D anomaly-free chiral matter theory of symmetry $G$?" In particular, we propose that the 3$_L$-5$_R$-4$_L$-0$_R$ U(1) chiral fermion theory, with two left-moving fermions of charge-3 and 4, and two right-moving fermions of charge-5 and 0 at low energy, can be put on a 1D spatial lattice where the U(1) symmetry is realized as an onsite symmetry, if we include properly designed multi-fermion interactions with intermediate strength. In general, we propose that any 1+1D U(1)-anomaly-free chiral matter theory can be defined as a finite system on a 1D lattice with onsite symmetry by using a quantum Hamiltonian with continuous time, but without suffering from Nielsen-Ninomiya theorem's fermion-doubling, if we include properly-designed interactions between matter fields. We propose how to design such interactions by looking for extra symmetries via bosonization/fermionization. We comment on the new ingredients and the differences of ours compared to Ginsparg-Wilson fermion, Eichten-Preskill, and Chen-Giedt-Poppitz (CGP) models, and suggest modifying CGP model to have successful mirror-decoupling. We show a topological non-perturbative proof of the equivalence between $G$-symmetric 't Hooft anomaly cancellation conditions and $G$-symmetric gapping rules (e.g. Haldane's stability conditions for Luttinger liquid) for multi-U(1) symmetry. We expect our result holds universally regardless of spatial Hamiltonian or Lagrangian/spacetime path integral formulation. Numerical tests are demanding tasks but highly desirable for future work.

Cosmological imprints of Dirac neutrinos in a keV-vacuum 2HDM* *Supported by the National Natural Science Foundation of China (12135006, 12075097, 12047527, 11775092), as well as by the Fundamental Research Funds for the Central Universities (CCNU20TS007, CCNU19TD012, CCNU22LJ004)

The Dirac neutrino masses could be simply generated by a neutrinophilic scalar doublet with a vacuum being dramatically different from the electroweak one. While the case with an eV-scale vacuum has been widely explored previously, we exploit in this work the desert where the scalar vacuum is of scale. In this regime, there would be rare hope to probe the keV-vacuum neutrinophilic scalar model via the lepton-flavor-violating processes, which makes it distinguishable from the widely considered eV-scale vacuum. Although such a keV-vacuum scenario is inert in the low-energy flavor physics, we show that the baryogenesis realized via the lightest Dirac neutrino can be a natural candidate in explaining the baryon asymmetry of the Universe. Furthermore, the Dirac neutrinos with a keV-vacuum scalar can generate a shift of the effective neutrino number within the range , which can be probed by the future Simons Observatory experiments. In particular, the model with a minimal value can already be falsified by the future CMB Stage-IV and Large Scale Structure surveys, providing consequently striking exploratory avenues in the cosmological regime for such a keV-vacuum scenario.

Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

To capture the universal low-energy physics of metals within effective field theories, one has to generalize the usual notion of scale invariance and renormalizable field theory due to the presence of intrinsic scales (Fermi momenta). In this paper, we develop a field-theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. The formalism is applied to the non-Fermi liquid that arises at the antiferromagnetic quantum critical point in two space dimensions. In the space of coupling functions, an interacting fixed point arises at a point with momentum-independent couplings and vanishing nesting angle. In theories deformed with non-zero nesting angles, coupling functions acquire universal momentum profiles controlled by the bare nesting angles at low energies before flowing to superconducting states in the low-energy limit. The superconducting instability is unavoidable because lukewarm electrons that are coherent enough to be susceptible to pairing end up being subject to a renormalized attractive interaction with its minimum strength set by the nesting angle irrespective of the bare four-fermion coupling. Despite the inevitable superconducting instability, theories with small bare nesting angles and bare four-fermion couplings that are repulsive or weakly attractive must pass through the region with slow RG flow due to the proximity to the non-Fermi liquid fixed point. The bottleneck region controls the scaling behaviours of the normal state and the quasi-universal pathway from the non-Fermi liquid to superconductivity. In the limit that the nesting angle is small, the non-Fermi liquid scaling dictates the physics over a large window of energy scale above the superconducting transition temperature.

Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

In this work we propose a \mathbb{Z}_NℤN clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with N^2N2 (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

Dynamical chiral magnetic current and instability in Weyl semimetals

Weyl semimetals realize massless relativistic fermions with two Weyl nodes separated in energy and momentum space, whose low-energy physics is described by Dirac fermions with an axial gauge constant. Here, we study their electromagnetic linear responses based on the effective field theory and on the chiral kinetic theory. Although the static chiral magnetic effect is canceled by the Chern-Simons current under the Pauli-Villars regularization, a dynamical magnetic field is found capable of driving an electric current along its direction, with the total transported charge being independent of temperature and chemical potential for a uniform field. We also incorporate dissipation in the relaxation-time approximation and study collective excitations coupled with Maxwell electromagnetic fields when Weyl node populations deviate from equilibrium. Their dispersion relations at low frequency and long wavelength are determined only by electric, chiral magnetic, and anomalous Hall conductivities, which predict unstable modes leading to anisotropic generation of electromagnetic waves oriented to the direction of Weyl node separation.

Network model for periodically strained graphene

The long-wavelength physics of monolayer graphene in the presence of periodic strain fields has a natural chiral scattering network description. When the strain field varies slowly compared to the graphene lattice and the effective magnetic length of the induced valley pseudomagnetic field, the low-energy physics can be understood in terms of valley-polarized percolating domain-wall modes. Inspired by a recent experiment, we consider a strain field with threefold rotation and mirror symmetries but without twofold rotation symmetry, resulting in a system with the connectivity of the oriented kagome network. Scattering processes in this network are captured by a symmetry-constrained phenomenological $S$ matrix. We analyze the phase diagram of the kagome network, and show that the bulk physics of the strained graphene can be qualitatively captured by the network when we account for a percolation transition at charge neutrality. We also discuss the limitations of this approach to properly account for boundary physics.

Quantum Floquet spectra of surface and bulk state of topological insulator

Topological insulator is a new class of material, which consists of insulating bulk and conducting surface state. In this study, we investigated the behaviour of bulk and surface state of topological insulator under a high frequency electromagnetic field, produce a kind of oscillation called as Floquet oscillation. We successfully identified the classical and quantum behavior of Floquet oscillation in the prospective of collapse revival spectra. This work shows the bulk and surface states behaviour of a topological insulator with the help of Floquet and Rabi frequency and describes the dominancy of Floquet oscillation in the low energy physics. Numerical simulation has been applied for verifying the Floquet approximation.

Nuclear structure data obtained by the (nth,2γ) reaction

The determination of nuclear structure parameters such as gamma transitions, level scheme, nuclear level density and radiative strength functions is one of the most important tasks in low-energy nuclear physics. The two-step gamma cascades method based on detection of gamma coincidences following neutron capture, ie. the (n,2γ) reaction has been proven to give spectroscopic data and data concerning level density and radiative strength function. This method allows for the study of the dynamics of interaction and inter-transition between Fermi-and Bose-states of the nucleus near the neutron binding energy. There is an essential difference between these intranuclear processes from those in classical and high-temperature superfluidity, which is determined by a shape of the investigated nucleus, the nucleon parity in it, existence of nucleons of different types (protons and neutrons) etc. Two-step gamma cascades technique has so far been successfully applied for 45 nuclei in the mass region 28<A<200. Brief description of the method will be included here with examples from the recent research

Gamma-ray track reconstruction using graph neural networks

Since the advent of the new generation of germanium detector arrays for low-energy nuclear physics experiments utilizing gamma-ray tracking, the challenges associated with track-reconstruction methods have been extensively studied. In the present work an approach based on recent developments in machine learning was used to address the problem. Here, a graph neural network was constructed and trained on data simulated in Geant4 in order to attempt track reconstruction of gamma rays below 1 MeV in a spherical shell geometry of pure germanium. Using a thick-shell geometry, and simulated data without energy- and position uncertainties the network achieved a reconstruction rate above 80% for complete tracks, and a combined peak-to-total value of 85% for energy spectra with four discrete peaks. For data with added noise, i.e. finite resolution in interaction-point position and energy, the corresponding peak-to-total ratio dropped to 74%. The track reconstruction was stable across multiplicities 1–10 but showed an increased error frequency in the energy range between 50 keV and 250 keV. To specifically study the complication of gamma tracks lost by out-scattering from the detector volume, a thin-shell (9 cm thickness) geometry was used together with a modified version of the GNN framework. By letting the GNN code identify and discriminate the out-scatter events, an improvement of the P/T value from 66% to 75% was found for the packed, noisy data. For the sake of comparison the new GNN model with existing gamma-ray tracking methods, a separate instance of the network was trained on slightly higher energies (up to 1.5 MeV) and multiplicities (up to 15) to evaluate 1.332 MeV photon cascade data in terms of P/T and photo-peak efficiency. The results for this GNN data set, with P/T values at 85% for single tracks and 74% for multiplicity 15, show clear promise when compared to the existing tracking methods.

Achieving the quantum field theory limit in far-from-equilibrium quantum link models

Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work \cite{zache2021achieving} has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of 1+1D U(1) quantum link models approaches the quantum field theory limit already at small link spin length S. Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.

Confinement phase in carbon-nanotubes and the extended massive Schwinger model

Carbon nanotube with electric fluxes confined in one dimension is studied. We show that a Coulomb interaction leads to a confinement phase with many properties similar to QCD in 4D. Low-energy physics is described by the massive Schwinger model with multi-species fermions labeled by the band and valley indices. We propose two means to detect this state. One is through an optical measurement of the exciton spectrum, which has been calculated via the ’t Hooft–Berknoff equation with the light-front field theory. We show that the Gell–Mann−Oakes−Renner relation is satisfied by a dark exciton. The second is the nonlinear transport which is related to Coleman’s ‘half-asymptotic’ state.

Transition from band insulator to Mott insulator and formation of local moment in the half-filled ionic SU(N) Hubbard model

We investigate the local moment formation in the half-filled SU($N$) Hubbard model under a staggered ionic potential. As the Hubbard $U$ increases, the charge fluctuations are suppressed and eventually frozen when $U$ is above a critical value $U_c$, marking the development of well-defined local moment with integer $m$ fermions on the A-sublattice and $(N-m)$ fermions on the B-sublattice, respectively. We obtain an analytical solution for $U_c$ for the paramagnetic ground state within the variational Gutzwiller approximation and renormalized mean field theory. For large $N$, $U_c$ is found to depend on $N$ linearly with fixed $m/N$, but sublinearly with fixed $m$. The local moment formation is accompanied by a peculiar phase transition from the band insulator to the Mott insulator, where the ionic potential and quasiparticle weight are renormalized to zero simultaneously. Inside the Mott phase, the low energy physics is described by the SU($N$) Heisenberg model with conjugate representations, which is widely studied in the literature.

Magnetic field effects on the quantum spin liquid behaviors of NaYbS2

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between and ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

Boundary theory of the X-cube model in the continuum

We study the boundary theory of the $\mathbb{Z}_N$ X-cube model using a continuum perspective, from which the exchange statistics of a subset of bulk excitations can be recovered. We discuss various gapped boundary conditions that either preserve or break the translation/rotation symmetries on the boundary, and further present the corresponding ground state degeneracies on $T^2\times I$. The low-energy physics is highly sensitive to the boundary conditions: even the extensive part of the ground state degeneracy can vary when different sets of boundary conditions are chosen on the two boundaries. We also examine the anomaly inflow of the boundary theory and find that the X-cube model is not the unique (3+1)d theory that cancels the 't Hooft anomaly of the boundary.

Gifts from anomalies: Exact results for Landau phase transitions in metals

Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, \mathbf{q}=0𝐪=0, is a constant independent of frequency, and the real part of the optical conductivity, \sigma(\omega)σ(ω), is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

Model with two scalar leptoquarks: R2 and S3

We discuss a model that can accommodate the $B$-physics anomalies, based on combining two scalar leptoquarks, ${R}_{2}$ and ${S}_{3}$, of mass $\mathcal{O}(1\text{ }\text{ }\mathrm{TeV})$, and that we proposed in our previous paper. We update the analysis of its parameter space and show that a model remains viable and consistent with a number of low energy and high energy flavor physics constraints. Since the model predicts a nonzero new physics phase, we discuss the possibility to test its contribution to the neutron electric dipole moment and to the angular distributions of the exclusive $b\ensuremath{\rightarrow}c\ensuremath{\tau}\overline{\ensuremath{\nu}}$ decays. We find that the model can provide a significant enhancement to $\mathcal{B}(B\ensuremath{\rightarrow}{K}^{(*)}\ensuremath{\nu}\ensuremath{\nu})$ and provides both the upper and lower bounds to $\mathcal{B}(B\ensuremath{\rightarrow}{K}^{(*)}\ensuremath{\mu}\ensuremath{\tau})$.

Correspondence of topological classification between quantum graph extra dimension and topological matter

In this paper, we study five-dimensional Dirac fermions of which extra-dimension is compactified on quantum graphs. We find that there is a non-trivial correspondence between matrices specifying boundary conditions at the vertex of the quantum graphs and zero-dimensional Hamiltonians in gapped free-fermion systems. Based on the correspondence, we provide a complete topological classification of the boundary conditions in terms of non-interacting fermionic topological phases. The ten symmetry classes of topological phases are fully identified in the language of five-dimensional Dirac fermions, and topological numbers of the boundary conditions are given. In analogy with the bulk-boundary correspondence in non-interacting fermionic topological phases, the boundary condition topological numbers predict four-dimensional massless fermions localized at the vertex of the quantum graphs and thus govern the low energy physics in four dimensions.

Anomalies of non-Abelian finite groups via cobordism

We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of ‘anomaly interplay’, which uses functoriality of cobordism and naturality of the η-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including S3, A4, Q8, and SL(2, \U0001d53d3).In the case of finite abelian groups, it is well known that anomalies can be ‘truncated’ in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with A4 symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the SL(2, \U0001d53d3) symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a ℤ/3 extension of SL(2, \U0001d53d3).

Many-body electronic structure of d9−δ layered nickelates

The recent observation of superconductivity in an infinite-layer and quintuple-layer nickelate within the same $R_{n+1}$Ni$_{n}$O$_{2n+2}$ series ($R$ = rare-earth, $n=2-\infty$, with $n$ indicating the number of NiO$_{2}$ layers along the $c$-axis), unlocks their potential to embody a whole family of unconventional superconductors. Here, we systematically investigate the many-body electronic structure of the layered nickelates (with $n=2-6,\infty$) within a density-functional theory plus dynamical mean-field theory framework and contrast it with that of the known superconducting members of the series and with the cuprates. We find that many features of the electronic structure are common to the entire nickelate series, namely, strongly correlated Ni-$d_{x^{2}-y^{2}}$ orbitals that dominate the low-energy physics, mixed Mott-Hubbard/charge-transfer characteristics, and $R$($5d$) orbitals acting as charge reservoirs. Interestingly, we uncover that the electronic structure of the layered nickelates is highly tunable as the dimensionality changes from quasi-two-dimensional to three-dimensional as $n \rightarrow \infty$. Specifically, we identify the tunable electronic features to be: the charge-transfer energy, presence of $R(5d)$ states around the Fermi level, and the strength of electronic correlations.

Nuclear Forces for Precision Nuclear Physics: A Collection of Perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.