Properties Of Fermions Research Articles

Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, H1(e,e′,π+)n [H. P. Blok (Jefferson Lab Fπ Collaboration), Charged pion form factor between Q2=0.60, and 2.45 GeV2. I. Measurements of the cross section for the H1(e,e′π+)n reaction, .], we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results [H.-M. Choi , Pion off-shell electromagnetic form factors: Data extraction and model analysis, .] from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F1(Q2,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q2,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties. Published by the American Physical Society 2024

Generalized boson and fermion operators with a maximal total occupation property

Abstract We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Three-dimensional topological insulators can be described by an effective field theory involving two ‘hydrodynamic’ Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form ℤ2 symmetry of the bosonic theory and its gauging, which originates the fermion number (−1)F, the spin sectors and the time reversal symmetry obeying T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}2 = (−1)F. These results are detailed for the effective action and the partition function on the geometry S2 × S1.

Study of shear Alfve’n waves with Landau quantization effect in degenerate relativistic plasma

In a ground breaking endeavor, we investigate a fundamental quantum property of fermions, specifically electrons, within a non-uniform quantized magnetic field, unveiling novel insights into shear Alfve’n waves in the relativistic realm of quantum plasma, particularly within the context of a degenerate Fermi gas. Employing the quantum magnetohydrodynamic model, we delve into the profound implications of the Landau quantization effect. This quantum phenomenon holds paramount importance across diverse fields such as condensed matter physics, astrophysics, and quantum information. Our study focuses on a plasma composed of degenerate relativistic electrons coexisting with cold fluid ions, which are non-degenerate particles. The findings of this research reveal substantial modifications in the thermodynamic, kinetic, and dispersion relation characteristics of shear Alfve’n waves when subjected to a non-uniform quantized magnetic field. This exploration offers a pioneering perspective on the intricate interplay between quantum physics and plasma dynamics, with implications for a wide array of scientific disciplines.

Geometric Algebra Jordan-Wigner Transformation for Quantum Simulation.

Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan-Wigner transformation (JWT) and the Bravyi-Kitaev transformation) correspond in a quantum circuit to the introduction of a supplementary circuit level. In order to include the fermionic properties in a more straightforward way in quantum computations, we propose to use methods issued from Geometric Algebra (GA), which, due to its commutation properties, are well adapted for fermionic systems. First, we apply the Witt basis method in GA to reformulate the JWT in this framework and use this formulation to express various quantum gates. We then rewrite the general one and two-electron Hamiltonian and use it for building a quantum simulation circuit for the Hydrogen molecule. Finally, the quantum Ising Hamiltonian, widely used in quantum simulation, is reformulated in this framework.

Ab Initio Path Integral Monte Carlo Simulations of the Uniform Electron Gas on Large Length Scales.

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, materials science, and related disciplines. At finite temperatures, the gold standard is given by ab initio path integral Monte Carlo (PIMC) simulations, which do not require any empirical input but exhibit an exponential increase in the required computation time for Fermionic systems with an increase in system size N. Very recently, computing Fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles has been suggested. In our work, we use this technique to perform very large (N ≤ 1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of the investigated properties, i.e., the static structure factor, the static density response function, and the local field correction, over the entire range of length scales.

Transport properties in gapped graphene through magnetic barrier in a laser field

We study the transport properties of Dirac fermions through gapped graphene through a magnetic barrier irradiated by a laser field oscillating in time. We use Floquet theory and the solution of Weber’s differential equation to determine the energy spectrum corresponding to the three regions composing the system. The boundary conditions and the transfer matrix approach are employed to explicitly determine the transmission probabilities for multi-energy bands and the associated conductance. As an illustration, we focus only on the three first bands: the central band T0 (zero photon exchange) and the two first side bands T±1 (photon emission or absorption). It is found that the laser field activates the process of translation through photon exchange. Furthermore, we show that varying the incident angle and energy gap strongly affects the transmission process. The conductance increases when the number of electrons that cross the barrier increases, namely when there is a significant transmission.

Tuning the Fermi surface of PrSb to enhance the interplay between superconductivity and magnetism by Sn substitution

The nature of Fermi surface in view of shapes and density of the nearest energy bands plays important role in tuning the physical and chemical properties of heavy fermions, Weyl metals, topological insulators, and superconductors. The interplay between superconductivity, magnetism, and fermionic nature of materials can be enhanced by modifying the shape of Fermi surface. The modification may be accomplished by tuning the surface topology, such as flatness and thickness, of electronic energy bands around the Fermi surface. Herein, we investigate the interplay between the magnetism, superconductivity, and heavy Fermionic nature of PrSb by tuning the shape of the Fermi surface by Sn substitution via PrSnxSb1-x (x = 0.0,0.25,0.50,0.75 &1.0) substitution scheme. For the theoretical designing of the materials and computation of the targeted properties, we implement density functional theory using the generalized–gradient approximation extended to the Perdew-Bruke-Ernzerhof correction to account for the exchange–correlation. The modification in the thickness and flatness of energy bands and density of states around the Fermi surface of PrSb compounds by changing the Sn/Pb substitution ratio, leads to simultaneous enhancement of the interplay between magnetism, superconductivity, and fermionic nature of the compounds.

Observation of fermionic time-reversal symmetry in acoustic topological metamaterials

In an electronic (fermionic) system, these chiral edge states (CESs) allow inversely polarized carriers to propagate in opposite directions at the edge of the topological insulators, which is related to the time-reversal symmetry (TRS) in fermionic systems. However, in acoustic (bosonic) systems, unlike those exhibited by fermionic systems, since there is no inherent polarization, it is generally believed that the CESs protected by fermionic TRS with independent counter-propagating cannot be supported. Herein, a strategy that achieves the counter-propagating CESs in topological metamaterials with fermionic TRS is reported in a 3D acoustic system. First, we designed a Floquet evolution protocol to incorporate effective fermionic TRS. Furthermore, by utilizing metamaterials, we creatively employ two subwavelength structures, that is, a cavity structure for adjusting the phase shift and a tube structure for providing coupling, which allows the model to be miniaturized. Finally, our experiment verifies the effectiveness of our approach. Our research results enrich the knowledge of topological metamaterials in the field of topological physics and pave the way for exploring fermionic properties in bosonic systems.

Topological Circular Dichroism in Chiral Multifold Semimetals.

Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and first-principles calculations. We show that, when the low-energy spectrum respects emergent SO(3) rotational symmetry, topological circular dichroism is forbidden for Weyl fermions, and thus is unique to chiral multifold fermions. This is a result of the selection rule that is imposed by the emergent symmetry under the combination of particle-hole conjugation and spatial inversion. Using first-principles calculations, we predict that topological circular dichroism occurs in CoSi for photon energy below about 0.2eV. Our Letter demonstrates the existence of a response property of unconventional fermions that is fundamentally different from the response of Dirac and Weyl fermions, motivating further study to uncover other unique responses.

Spectral properties and exact solutions for Rabi-coupled noninteracting fermions in a spin-dependent anharmonic trapping potential

We investigate the effect of spin-motion coupling on the spectral properties of Rabi-coupled noninteracting fermions in a spin-dependent harmonic trapping potential plus an anharmonic term. It is shown that when the spin-motion coupling becomes strong, fermions tend to stay in one of the two components. In the limit of the strong spin-motion coupling, the entire energy spectrum exhibits a sequence of near degeneracy. In particular, in the case of the sextic anharmonic term, the system admits the exact analytical energies and wave functions of the bound states for an infinite number of the specific parameter conditions. The properties of the energy spectrum have also been discussed on basis of these obtained exact analytical solutions.

Valley conductance and reflection probabilities in substrate-induced graphene superlattice

We study the transport properties of mass-less and spin-less Dirac fermions in a substrate-induced graphene super-lattice. The tight binding model for the super-lattice gives the energy band structure and we classify the topological regions (trivial and non-trivial) depending on the topological order parameter. The transfer matrix approach is used to compute the probabilities of the reflection and transmission in terms of structural parameters and we investigate the valley-switching phenomenon for all values of incident electron energies (E). We observe that the Dirac fermions with valley degree of freedom sometimes completely and other times partially reflect and transmit to the other valley under some specific values of structure parameters suggesting that we have a finite value of switching probability (≤100%) for all values of E. Moreover, the conductance exhibits striking behaviour, showing a peak at each Dirac point, which merges and subsequently vanishes depending on the structure parameters.

Spinor domain wall and test fermions on an arbitrary domain wall

We consider a spinor domain wall embedded in a five-dimensional spacetime with a nondiagonal metric. The corresponding plane symmetric solutions for linear and nonlinear spinor fields with different parameters are obtained. It is shown that in the general case the metric functions and spinor fields do not possess Z_2 symmetry with respect to the domain wall. We study the angular momentum density of the domain wall arising because of the presence of the spinor field creating the wall. The properties of test fermions located on an arbitrary domain wall are considered. The concepts of the “second spin” (arising due to the properties of the Lorentz group generators in a five-dimensional spacetime) and of the “second magnetic field” (representing the components F_{i 5} of the electromagnetic field five-tensor) are introduced. We find eigenspinors of the “second spin” and show that some of them represent the Bell states. In the nonrelativistic limit we derive the Pauli equation for the test fermions on the domain wall which contains an extra term describing the interaction of a spin-1/2 particle with the “second magnetic field”; this allows the possibility of an experimental verification of the existence of extra dimensions.

Thermodynamics of fermions at any temperature based on parametrized partition function.

In this work, we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three-dimensional space defined by energy, temperature, and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of Fermi systems with numerical simulation. As an example, we present energies and heat capacities for 10 noninteracting fermions and 10 interacting fermions and show good agreement with the analytical result for the noninteracting case.

Highly anisotropic Dirac fermion and spin transport properties in Cu-graphane

Inspired by the successful synthesis of hHv-graphane [Nano Lett. 15 903 (2015)], a new two-dimensional (2D) Janus material Cu-graphane is proposed based on the first-principles calculations. Without the spin–orbit coupling (SOC) effect, Cu-graphane is a Dirac semimetal with a highly anisotropic Dirac cone, whose Fermi velocity ranges from 0.12 × 105 m/s to 2.9 × 105 m/s. The Dirac cone near the Fermi level can be well described with an extended 2D Dirac model Hamiltonian. In the presence of the SOC effect, band splitting is observed around the Fermi level, and a large intrinsic spin Hall conductivity (ISHC) with a maximum value of 346 (ℏ/e) S/cm is predicted. Moreover, the spin Hall transport can be regulated by slightly adjusting the Fermi energy, e.g., grid voltage or chemical doping. Our work not only proposes a new 2D Janus material with a highly anisotropic Dirac cone and a large ISHC, but also reveals that a large ISHC may exist in some Dirac systems.

Thermofield Theory for Finite-Temperature Electronic Structure.

Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. They also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.

Singular Limits of Relative Entropy in Two Dimensional Massive Free Fermion Theory

We show that certain singular limits of relative entropy of vacuum states in two dimensional massive free fermion theory exist and compute these limits. As an application we show that the c function computed by Casini and Huerta based on heuristic arguments arise naturally as a consequence of our results.

Solving 2D and 3D Lattice Models of Correlated Fermions—Combining Matrix Product States with Mean-Field Theory

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute Tc for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The MPS+MF framework thus enables the quantitative study of USC and high-Tc superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., Tc due to its mean-field component, is near constant in microscopic parameters. These features of the MPS+MF approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.13 MoreReceived 8 July 2022Revised 7 December 2022Accepted 3 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011039Published 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 AreasFermionsSuperconductivityPhysical Systems3-dimensional systemsStrongly correlated systemsUnconventional superconductorsTechniquesBosonizationDensity matrix renormalization groupMean field theoryCondensed Matter, Materials & Applied Physics

Confined vs. extended Dirac surface states in topological crystalline insulator nanowires

Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host multiple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the \langle 100 \rangle‹100› type display novel Aharonov-Bohm oscillations, while nanowires with the four facets of the \langle 110 \rangle‹110› type such oscillations are absent due to strong confinement of the Dirac states to each facet separately. Our results place TCI nanowires as a versatile platform for confining and manipulating Dirac surface states.

Emerging D massive graviton in graphene-like systems

Unlike the fundamental forces of the Standard Model the quantum effects of gravity are still experimentally inaccessible. Rather surprisingly quantum aspects of gravity, such as massive gravitons, can emerge in experiments with fractional quantum Hall liquids. These liquids are analytically intractable and thus offer limited insight into the mechanism that gives rise to quantum gravity effects. To thoroughly understand this mechanism we employ a graphene-like system and we modify it appropriately in order to realise simple -dimensional massive gravity model. More concretely, we employ -dimensional Dirac fermions, emerging in the continuous limit of a fermionic honeycomb lattice, coupled to massive gravitons, simulated by bosonic modes positioned at the links of the lattice. The quantum character of gravity can be determined directly by measuring the correlations on the bosonic atoms or by the interactions they effectively induce on the fermions. The similarity of our approach to current optical lattice configurations suggests that quantum signatures of gravity can be simulated in the laboratory in the near future, thus providing a platform to address question on the unification theories, cosmology or the physics of black holes.