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The Jordan–Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan–Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J1–J2 Heisenberg models, as well as to the pairing or reduced Bardeen–Cooper–Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians. [ABSTRACT FROM AUTHOR]

Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi–Dirac theory; thermal Hartree–Fock (HF) theory; two modifications of the thermal single-determinant approximation of Kaplan and Argyres, Ann. Phys. 92, 1–24 (1975); and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Thermal full-configuration-interaction theory is used as the benchmark. [ABSTRACT FROM AUTHOR]

Five time-dependent orbital optimized coupled-cluster methods, of which four can converge to the time-dependent complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers. Truncation schemes maintaining the intragroup orbital rotation invariance, as well as equations of motion of coupled-cluster (CC) amplitudes and orbitals, are derived. Present methods are compact CC-parameterization alternatives to the time-dependent multiconfiguration self-consistent-field method for systems consisting of arbitrarily different kinds and numbers of interacting fermions. Theoretical analysis of applications of present methods to various chemical systems is reported. [ABSTRACT FROM AUTHOR]

In this work, we present the investigation of the magnetotransport properties of a capped SnTe film, grown by molecular beam epitaxy, using Shubnikov–de Haas oscillations for the detection of Dirac fermions. The cap layer used was a 10 nm thick Sn0.98Eu0.02Te film, which can also contribute to the transport such that it is mandatory to isolate its contribution from the electrical transport measured in the sample. To separate the contribution from both layers, photoconductivity measurements were performed. A detailed analysis of the Shubnikov–de Haas oscillations is carried out using theoretical expressions and building the Landau-level indexation. We found that Dirac fermions are detected in the SnTe layer, while the cap layer contributes with trivial fermions, protecting SnTe against deterioration due to exposure to the atmosphere. [ABSTRACT FROM AUTHOR]

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan–Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree–Fock–Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. We also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians. [ABSTRACT FROM AUTHOR]

In this note, we discuss an analogy between the BCS theory and the seesaw model of neutrinos. We believe that the analogy indicates some fundamental aspects of Majorana neutrinos. A paper on the issue has been recently presented, and we would like to describe the background of the paper together with our personal views on the problem. In essence, the conventional construction of a Majorana neutrino from a chiral fermion is too simplified, and we argue that one would actually have to go through a Bogoliubov-type canonical transformation to generate two Majorana fermions from an effective single Dirac fermion in the seesaw model. [ABSTRACT FROM AUTHOR]

For a quasi-bialgebra H , we show that the category C of H -bimodules is duoidal and that the so called u-coaugmented bimonoids in C are exactly the quasi-bialgebras with a coalgebra projection. When H is a quasi-Hopf algebra with bijective antipode, we prove that the u-coaugmented bimonoids in C can also be described as what we will call double wreath quasi-Hopf algebras, objects determined by H and pre-bialgebras R within the category of Yetter-Drinfeld modules over H. A particular class of double wreath quasi-Hopf algebras is obtained by deforming with a 2-cocycle the multiplication of a Radford biproduct quasi-Hopf algebra. Other classes of this type are given by the symplectic fermion quasi-Hopf algebras. [ABSTRACT FROM AUTHOR]

Driven quantum materials often feature emergent topology, otherwise absent in static crystals. Dynamic bulk-boundary correspondence, encoded by nondissipative gapless modes residing near the Floquet zone center and/or boundaries, is its most prominent example. Here we show that topologically robust gapless dispersive modes appear along the grain boundaries, embedded in the interior of Floquet topological crystals, when the Floquet-Bloch band inversion occurring at a finite momentum ( K inv Flq ) and the Burgers vector (b ) of the constituting array of dislocations satisfy K inv Flq · b = π (modulo 2 π ). Such nondissipative gapless states can be found near the center and/or edges of the Floquet Brillouin zone, irrespective of the drive protocol. We showcase these general outcomes for two-dimensional driven time-reversal symmetry breaking insulators. Promising experimental platforms hosting such dynamic topological dispersive bands in real materials are discussed. [ABSTRACT FROM AUTHOR]

A model is presented where a GeV axion‐like‐particle (ALP) is predicted in a large portion of the parameter space due to the presence of explicit Peccei–Quinn (PQ) symmetry‐breaking terms in an exotic leptonic sector. The latter provides a solution to the muon g−2$g-2$ anomaly, within the framework of the Linear Seesaw neutrino mechanism. The spectrum is extended by a complex scalar singlet only transforming under the PQ symmetry, which generates the ALP. Its couplings with fermions can continuously span over many orders of magnitude, which constitutes a specific feature of this model in contrast to generic ultraviolet constructions. Interestingly, these couplings are suppressed by the ALP characteristic scale that can be as low as the TeV scale, which represents a novel feature of the model and opens up to several phenomenological consequences. [ABSTRACT FROM AUTHOR]

Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources flow within a network, fundamentally shaping the behavior of dynamical processes and distinguishing directed networks from their undirected counterparts. Robust null models are crucial for identifying meaningful patterns in these representations, yet designing models that preserve key features remains a significant challenge. One such critical feature is reciprocity, which reflects the balance of bidirectional interactions in directed networks and provides insights into the underlying structural and dynamical principles that shape their connectivity. This paper introduces a statistical mechanics framework for directed networks, modeling them as ensembles of interacting fermions. By controlling the reciprocity and other network properties, our formalism offers a principled approach to analyzing directed network structures and dynamics, introducing new perspectives and models and analytical tools for empirical studies. [ABSTRACT FROM AUTHOR]

We prove local (in space and time) well-posedness for a mildly regularised version of the stochastic quantisation of the Yukawa 2 Euclidean field theory with a self-interacting boson. Our regularised dynamic is still singular but avoids non-local divergences, allowing us to use a version of the Da Prato–Debussche argument (Da Prato and Debussche in Ann Probab 31(4):1900–1916, 2003. https://doi.org/10.1214/aop/1068646370). This model is a test case for a non-commutative probability framework for formulating the kind of singular SPDEs arising in the stochastic quantisation of field theories mixing both bosons and fermions. [ABSTRACT FROM AUTHOR]

When a system consists of a large subsystem (bath) and a small one (probe), thermalization implies induction of temperature of the bath onto the probe. If both the bath and the probe are described by same microscopic Hamiltonian, thermalisation further entails that the probe imbibes the phase of the bath. We refer to this phenomenon as phase thermalization. However, it is not clear whether this phenomenon is realizable when the probe and the bath are described by different microscopic Hamiltonians. We show phase thermalization is possible even when the microscopic Hamiltonians differ significantly. We provide an explicit example, where the probe is a Fermi liquid realised by a Majorana chain with n ≫ 1 fermions per site interacting through random hopping and the bath is an incoherent metal described by another Majorana chain with N > n fermions per site interacting through arbitrarily long range random four-fermion interaction. In deep infrared (i.e. at very low energies), the probe turns into an incoherent metal, with Lyapunov spectrum and diffusion coefficient identical to the bath. [ABSTRACT FROM AUTHOR]

An exact Jordan–Wigner type of transformation is presented in 1D connecting spin-1/2 operators to spinful canonical Fermi operators. The transformation contains two free parameters allowing a broad interconnection possibility between spin models and fermionic models containing spinful Fermi operators. [ABSTRACT FROM AUTHOR]

We investigate a cosmological model using the covariant formalism proposed by Canuto et al., considering bosonic and fermionic fields as sources, including both self-interacting potentials. Following that path, it is possible to determine, first, a family of symmetries using the Noether procedure. That permits to obtain the conformal function β(t), part of the covariant formalism, that maps the physics between descriptions. In gravitational units (old universe) it is verified that the bosonic/fermionic combination behaves as a dark constituent. In atomic units what emerges is an initially accelerated universe, followed a decelerated period, that would correspond to a primordial era considered as an analog of inflation. [ABSTRACT FROM AUTHOR]

The planar Thirring model is thought to have a strongly coupled critical point for a single flavor of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterization via an equation of state. Since the computation is numerically challenging, we investigate the improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte-Carlo scheme, and calculations of the bilinear condensate, an equation of state and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered. [ABSTRACT FROM AUTHOR]

In this paper, we will prove a series of q -identities suggested by the realisation of certain conformal field theories involving the so-called 'coupled free fermions.' We will consider q -series arising from coupled free fermions constructed by the parafermion coset construction as well as from scaled root lattices, and some interesting relations between the two. [ABSTRACT FROM AUTHOR]

The low energy manifold for fermions at finite density is the Fermi surface. I describe renormalization group (RG) in which modes encountered on approaching the Fermi surface are systematically integrated out. The fixed point is described by strictly marginal coupling functions identified as the Landau parameters and marginally relevant coupling functions describing the BCS instability in various angular momentum channels. [ABSTRACT FROM AUTHOR]

The modular flavor symmetry is studied to explain the mass hierarchy of quarks and leptons. In this review, at first, we introduce briefly the framework of the modular symmetries and its residual symmetries, and then, present the general framework of generating the mass hierarchy close to the symmetric points of modulus without fine-tuning. Finally, we present a minimal Γ 3 modular invariant model of quarks. We then describe how to obtain the hierarchical quark mass patterns in the vicinity of τ 0 = i ∞ and investigate the flavor structure of the quark mass matrices. The results of our study show that describing correctly the quark mass hierarchies without severe fine-tuning and the CP violation is remarkably challenging within the modular invariance approach to flavors. [ABSTRACT FROM AUTHOR]

Tunable quantum materials hold great potential for applications. Of special interest are materials in which small lattice strain induces giant electronic responses. The kagome compounds AV3Sb5 (A = K, Rb, Cs) provide a testbed for electronic tunable states. In this study, through angle-resolved photoemission spectroscopy, we provide comprehensive spectroscopic measurements of the electronic responses induced by compressive and tensile strains on the charge-density-wave (CDW) and van Hove singularity (VHS) in CsV3Sb5. We observe a tripling of the CDW gap magnitudes with ~ 1% strain. Simultaneously, changes of both energy and mass of the VHS are observed. Combined, this reveals an anticorrelation between the unconventional CDW order parameter and the mass of the VHS, and highlight the role of the latter in the superconducting pairing. The substantial electronic responses uncover a rich strain tunability of the versatile kagome system in studying quantum interplays under lattice variations. The authors report that tensile strain applied to CsV3Sb5 strongly suppresses the charge-density-wave (CDW) gap, increases the mass of the fermions at the higher-order van Hove singularity (HO-VHS) and drives the energy of the HO-VHS towards the Fermi energy. Further, they suggest an important role of the HO-VHS in superconducting pairing. [ABSTRACT FROM AUTHOR]

We show that the affine vertex superalgebra V k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) at generic level 푘 embeds in the equivariant 풲-algebra of s ⁢ p 2 ⁢ n times 4 ⁢ n free fermions. This has two corollaries: (1) it provides a new proof that, for generic 푘, the coset Com ⁡ (V k ⁢ (s ⁢ p 2 ⁢ n ) , V k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n )) is isomorphic to W ℓ ⁢ (s ⁢ p 2 ⁢ n ) for ℓ = − (n + 1) + (k + n + 1) / (2 ⁢ k + 2 ⁢ n + 1) , and (2) we obtain the decomposition of ordinary V k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) -modules into V k ⁢ (s ⁢ p 2 ⁢ n ) ⊗ W ℓ ⁢ (s ⁢ p 2 ⁢ n ) -modules. Next, if 푘 is an admissible level and ℓ is a non-degenerate admissible level for s ⁢ p 2 ⁢ n , we show that the simple algebra L k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) is an extension of the simple subalgebra L k ⁢ (s ⁢ p 2 ⁢ n ) ⊗ W ℓ ⁢ (s ⁢ p 2 ⁢ n ) . Using the theory of vertex superalgebra extensions, we prove that the category of ordinary L k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) -modules is a semisimple, rigid vertex tensor supercategory with only finitely many inequivalent simple objects. It is equivalent to a certain subcategory of W ℓ ⁢ (s ⁢ p 2 ⁢ n ) -modules. A similar result also holds for the category of Ramond twisted modules. Due to a recent theorem of Robert McRae, we get as a corollary that categories of ordinary L k ⁢ (s ⁢ p 2 ⁢ n ) -modules are rigid. [ABSTRACT FROM AUTHOR]

The aim of this study is to explore the potential which arises in a graphene–insulator–graphene structure when an external charged particle is moving parallel to it with a speed smaller than the Fermi speed in graphene. This is achieved by employing the dynamic polarization function of graphene within the random phase approximation, where its π electrons are modeled as Dirac fermions, and utilizing a local dielectric function for bulk insulators. Three different insulators are considered: SiO2, HfO2, and Al2O3. It is observed that the wake potential is induced by the surface optical phonons originating from the insulator layer, and that total potential could be effectively decomposed into two components, each corresponding to different phonon branches, as long as those branches do not interact amongst themselves. [ABSTRACT FROM AUTHOR]

We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1-dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, although it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag–Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme. [ABSTRACT FROM AUTHOR]

In a combined mean-field and semiclassical regime, we consider the time evolution of N fermions interacting through singular pair interaction potentials of the form j, which includes the Coulomb and gravitational interactions. We prove that the many-body dynamics of mixed states are well approximated by solutions of the Hartree-Fock and Vlasov equations in terms of Schatten norms. The errors in these approximations are expressed in terms of the expected number of particles, N, and the Planck constant, h. For cases where a 2 .0;1=2/, we obtain local-in-time results when N1=2 \ h ≤ N1=3. Notably, this leads to the derivation of the Vlasov equation with singular potentials. For cases where a ∈ [1/2, 1], our results hold only within a small time scale or require an N-dependent cut-off. A fundamental ingredient in our analysis is the propagation of regularity for solutions to the Hartree-Fock equation uniformly in the Planck constant, which holds for a ∈ (0, 1]. [ABSTRACT FROM AUTHOR]

In the context of braneworld scenarios, the real scalar field plays a crucial role by providing thickness for brane. In this work, we investigate a codimension-one thick brane within the framework of f(R, Q, P) gravity, where R represents the curvature scalar, while Q = R μ ν R μ ν and P = R μ ν α β R μ ν α β are quadratic geometric invariants. Our interest is to investigate the influence of these invariants on the scalar field solution and the energy density of the brane. Furthermore, we analyze the localization of spin 1/2 fermions and the gravitino by employing a Yukawa-like coupling with the scalar field background. Such a coupling is able to produce a normalizable zero-mode for both fields. [ABSTRACT FROM AUTHOR]

In this work, we have studied the vector scotogenic model in the context of the dark matter problem. Due to unitarity considerations, we have focused on the scenario with fermion dark matter, finding out that co-annihilations play a fundamental role in achieving dark matter relic abundance. Moreover, the coannihilation effects allow to separate the parameter space into two regions with different phenomenology. In addition, we have studied the detection prospects of these regions separately, focusing on signatures that can appear in lepton flavor violating decays, indirect and direct searches, and the production of these new particles at collider facilities. [ABSTRACT FROM AUTHOR]

Intrinsic spin of fermions can generate torsion in spacetime. This torsion is a non-propagating field that can be integrated out, leaving an effective non-universal four-fermion interaction. This geometrical interaction affects fermions inside a matter distribution and can be expected to become stronger as the density grows. We investigate the role of this interaction in a gravitationally collapsing fermionic distribution, by considering a statistical average of the interaction term which incorporates the effect of mixed vector and axial currents. We consider a gravitationally collapsing distribution of massive fermions, ignoring other interactions. Using simplified yet reasonable assumptions, we establish that the contribution can be attractive or repulsive depending on how torsion couples with different chiralities. Also, the interaction starts to dominate as the collapse proceeds, accelerating or decelerating the collapse depending on the relative signs of the geometrical interaction between different species of fermions. [ABSTRACT FROM AUTHOR]

We revisit an economical model for the g - 2 anomaly featuring a vector-like charged fermion, a scalar doublet and a scalar singlet in the light of new results from Fermilab. The phenomenological implications for lepton-flavor universality, Higgs decays, and charged lepton-flavor violating decays are discussed in detail. [ABSTRACT FROM AUTHOR]

We investigate the structure of the minimal left-right symmetric model that enables precise predictions in the gauge, scalar and neutrino sector. We revisit the complete set of mass spectra and mixings for the charged and neutral gauge bosons, would-be-Goldstones and gauge fixing, together with the ghost Lagrangian. In the scalar sector, we analytically re-derive all the massive states with mixings and devise a non-trivial physical input scheme, expressing the model couplings in terms of masses and mixing angles. Fermion couplings are also determined in closed form, including the Dirac mixing in the neutrino sector, evaluated explicitly using the Cayley–Hamilton theorem. These analytic developments are implemented in a comprehensive FeynRules model file. We calculate the one loop QCD corrections and provide a complete UFO file for NLO studies, demonstrated on relevant hadron-collider benchmarks. We provide various restricted variants of the model file with different gauges, massless states, neutrino hierarchies and parity violating g L ≠ g R gauge couplings. [ABSTRACT FROM AUTHOR]

In this paper we consider a modified quantum Boltzmann equation with the quantum effect measured by a continuous parameter \delta that can decrease from \delta =1 for the Fermi-Dirac particles to \delta =0 for the classical particles. In case of soft potentials, for the corresponding Cauchy problem in the whole space or in the torus, we establish the global existence and uniqueness of non-negative mild solutions in the function space L^{\infty }_{T}L^{\infty }_{v,x}\cap L^{\infty }_{T}L^{\infty }_{x}L^1_v with small defect mass, energy and entropy but allowed to have large amplitude up to the possibly maximum upper bound F(t,x,v)\leq \frac {1}{\delta }. The key point is that the obtained estimates are uniform in the quantum parameter 0< \delta \leq 1. [ABSTRACT FROM AUTHOR]

15 exactly solvable inhomogeneous (spinless) fermion systems on 1D lattices are constructed explicitly based on the discrete orthogonal polynomials of the Askey scheme, e.g. Krawtchouk, Hahn, Racah, Meixner, and q -Racah polynomials. The Schrödinger and Heisenberg equations are solved explicitly, as the entire set of the eigenvalues and eigenstates are known explicitly. The ground-state two-point correlation functions are derived explicitly. The multipoint correlation functions are obtained by Wick's theorem. 15 corresponding exactly solvable XX spin systems are also displayed. They all have nearest-neighbor interactions. The exact solvability of the Schrödinger equation means that the corresponding Fokker–Planck equation is also exactly solvable. This leads to 15 exactly solvable birth and death fermions and 15 birth and death spin models. These provide plenty of material for calculating interesting quantities, e.g. entanglement entropy, etc. [ABSTRACT FROM AUTHOR]

We show that the affine vertex superalgebra V k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) at generic level 푘 embeds in the equivariant 풲-algebra of s ⁢ p 2 ⁢ n times 4 ⁢ n free fermions. This has two corollaries: (1) it provides a new proof that, for generic 푘, the coset Com ⁡ (V k ⁢ (s ⁢ p 2 ⁢ n ) , V k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n )) is isomorphic to W ℓ ⁢ (s ⁢ p 2 ⁢ n ) for ℓ = − (n + 1) + (k + n + 1) / (2 ⁢ k + 2 ⁢ n + 1) , and (2) we obtain the decomposition of ordinary V k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) -modules into V k ⁢ (s ⁢ p 2 ⁢ n ) ⊗ W ℓ ⁢ (s ⁢ p 2 ⁢ n ) -modules. Next, if 푘 is an admissible level and ℓ is a non-degenerate admissible level for s ⁢ p 2 ⁢ n , we show that the simple algebra L k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) is an extension of the simple subalgebra L k ⁢ (s ⁢ p 2 ⁢ n ) ⊗ W ℓ ⁢ (s ⁢ p 2 ⁢ n ) . Using the theory of vertex superalgebra extensions, we prove that the category of ordinary L k ⁢ (o ⁢ s ⁢ p 1 | 2 ⁢ n ) -modules is a semisimple, rigid vertex tensor supercategory with only finitely many inequivalent simple objects. It is equivalent to a certain subcategory of W ℓ ⁢ (s ⁢ p 2 ⁢ n ) -modules. A similar result also holds for the category of Ramond twisted modules. Due to a recent theorem of Robert McRae, we get as a corollary that categories of ordinary L k ⁢ (s ⁢ p 2 ⁢ n ) -modules are rigid. [ABSTRACT FROM AUTHOR]

A master equation containing a nonlinear term that gives rise to disentanglement has been recently explored. Here, a modified version, which is applicable for indistinguishable particles, is proposed, and studied for both the Bose–Hubbard and the Fermi–Hubbard models. It is found for both Bosons and Fermions that disentanglement can give rise to quantum phase transitions. [ABSTRACT FROM AUTHOR]

Fermion functional integrals are calculated for the Dirac operator of a finite real spectral triple. Complex, real and chiral functional integrals are considered for each KO-dimension where they are non-trivial, and phase ambiguities in the definition are noted. [ABSTRACT FROM AUTHOR]

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of anyons in one dimension remains largely unexplored. In this work, we realize Abelian anyons in one dimension with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase through a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks and observe the anyonic Hanbury Brown-Twiss effect as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of one-dimensional anyons. [ABSTRACT FROM AUTHOR]

In this paper we suggest a possible explanation of the giant temperature peak in the amplitude of the de Haas–van Alphen oscillations observed at very low temperatures in insulating SmB6 system. Our theoretical model consists of two fermions with particle-like dispersion but with different masses, one much heavier than the other, which hybridize with each other to open up a gap at their degeneracy point. As a result of the hybridization a heavy-fermion hybrid appears at the Fermi level. Our results strongly suggest that it is exactly this heavy-fermion hybrid which results in the giant temperature peak. In addition we propose a scenario when this hybrid has edge states. [ABSTRACT FROM AUTHOR]

The generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model. On the cubic and hypercubic lattices the generating function is still unknown and the problem remains open. It has been conjectured that the three-dimensional (3D) and higher dimensional problems are not solvable—or, to be more precise, that there are no differentiably finite (D-finite) solutions. In this context, very recently a Berezin integral of an exponentiated Grassmann action was found for the polygon generating function on the cubic lattice, making explicit the connection between 3D polygons and a model of interacting fermions. Here we address the problem of how to generalize the 3D result to higher dimensions. We derive a Grassmann representation in terms of a Berezin integral for the generating function of polygons on d-dimensional hypercubic lattices. On the one hand, this new result admittedly brings us no closer to the problem of finding an explicit analytic expression for the desired generating function for polygons. On the other hand, however, the significant advance reported here precisely quantifies the remarkable mathematical difficulty of finding the explicit generating function. Indeed, the non-quadratic functional form of the Grassmann action that we derive here provides a very clear picture of the formidable mathematical obstruction that would need to be overcome. Specifically, in d dimensions, the Grassmann action contains terms of degree 2 (d - 1) , so the model describes interacting rather than free fermions. It is an open problem whether or not these models of interacting fermions can in principle be free fermionized through some still undiscovered algebraic method, but it is widely believed that this goal is mathematically impossible. [ABSTRACT FROM AUTHOR]

This contribution sets out to pursue the investigation of a supersymmetric electrodynamics model with Lorentz‐symmetry violation (LSV) manifested by a space‐time unbalance in the propagation of the fermionic charged matter. Despite violation of Lorentz symmetry, the supersymmetry algebra is kept untouched. A superspace approach is then adopted to build up an N=1$\mathcal {N}=1$‐supersymmetric Abelian gauge theory in presence of a Lorentz‐violating background supermultiplet that accommodates the space‐time asymmetry parameter of the charged matter. It is described, in this scenario, how the particular Lorentz‐symmetry breaking, brought about by the fermionic matter, affects its (matter) scalar partners and the photon/photino that minimally couple to charged matter. From the (modified) Dirac, Klein–Gordon and Maxwell field equations, the corresponding dispersion relations are worked out to inspect and discuss the physical effects of the LSV Majorana fermion condensates that naturally emerge from the background supermultiplet. Finally, efforts are targeted to investigate the Gordon decomposition of the charged lepton electromagnetic current. This is carried out by iterating the (fermion and scalar) matter field equations, which points to an effective contribution to the electron's electric dipole moment. This result allows us to attain an estimate of the pseudo‐vector condensate of the (LSV) Majorana background fermion. [ABSTRACT FROM AUTHOR]

We study ground states of a relativistic Fermi system involved with the pseudo-differential operator - c 2 Δ + c 4 m 2 - c 2 m in the L 2 -subcritical case, where m > 0 denotes the rest mass of fermions, and c ≥ 1 represents the speed of light. By employing Green's function and the variational principle of many-fermion systems, we prove the existence of ground states for the system. The asymptotic behavior of ground states for the system is also analyzed in the non-relativistic limit where c → ∞ . [ABSTRACT FROM AUTHOR]

We build an extended two Higgs doublet model theory with spontaneously broken |$U(1) _{X}$| global symmetry, where the tree-level universal seesaw mechanism generates the mass hierarchy of the Standard Model charged fermions and the Zee–Babu mechanism produces tiny active neutrino masses. The third family of SM charged fermions gets tree-level masses from Yukawa interactions involving the Higgs doublets |$H_1$| (for the top quark) and |$H_2$| (for the bottom quark and tau lepton). The model under consideration is consistent with SM fermion masses and mixings, with the muon and electron |$g-2$| anomalies, and successfully accommodates the constraints arising from charged-lepton-flavor violation and meson oscillations. The proposed model predicts rates for charged-lepton-flavor-violating decays within the reach of forthcoming experiments. [ABSTRACT FROM AUTHOR]