Fermion Pairs Research Articles

Fermion condensation and super pivotal categories

We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases that contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions and condensing pairs of physical and emergent fermions. There are two distinct types of objects in the resulting fermionic fusion categories, which we call “m-type” and “q-type” objects. The endomorphism algebras of q-type objects are complex Clifford algebras, and they have no analogs in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations arising from the condensed theories. We prove a series of results relating data in fermionic theories to data in their parent bosonic theories; for example, if C is a modular tensor category containing a fermion, then the tube category constructed from the condensed theory satisfies Tube(C/ψ)≅C×(C/ψ). We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the SO(3)6 theory, and the 12E6 theory and compute the quasiparticle excitation spectrum in each of the condensed theories.

Mean-field theory for fermion pairs and the ab initio particle-vibration coupling approach

A Dyson Bethe-Salpeter equation (Dyson-BSE) for fermion pairs is presented whose kernel has a static and a one frequency dependent contribution, analogous to the self energy of the single particle Dyson equation with the (static) mean field term and the energy dependent correlation term. The static part of the Dyson-BSE is the self-consistent mean field for the vibrations. At the same time, for the correlated single particle self-energy a full particle-vibration coupling (PVC) scattering equation is established where the vibration is the same as obtained from the Dyson-BSE. Both equations, single particle Dyson equation and Dyson-BSE, are coupled through self-consistency. Numerical results for Lipkin and 1D Hubbard chain are very promising.

Remarks on the mean-field theory based on the SO(2N + 1) Lie algebra of the fermion operators

Toward a unified algebraic theory for mean-field Hamiltonian describing paired- and unpaired-mode effects, in this paper, we propose a generalized Hartree–Bogoliubov mean-field Hamiltonian in terms of fermion pair and creation-annihilation operators of the [Formula: see text] Lie algebra. We diagonalize the generalized Hartree–Bogoliubov mean-field Hamiltonian and throughout its diagonalization we can first obtain the unpaired mode amplitudes which are given by the self-consistent field parameters appeared in the Hartree–Bogoliubov theory together with the additional self-consistent field parameter in the generalized Hartree–Bogoliubov mean-field Hamiltonian and by the parameter specifying the property of the [Formula: see text] group. Consequently, it turns out that the magnitudes of these amplitudes are governed by such parameters. Thus, it becomes possible to make clear a new aspect of such results. We construct the Killing potential in the coset space [Formula: see text] on the Kähler symmetric space which is equivalent to the generalized density matrix. We show another approach to the fermion mean-field Hamiltonian based on such a generalized density matrix. We derive an [Formula: see text] generalized Hartree–Bogoliubov mean-field Hamiltonian operator and a modified Hartree–Bogoliubov eigenvalue equation. We discuss on the mean-field theory related to the algebraic mean-field theory based on the generalized density matrix and the coadjoint orbit leading to the nondegenerate symplectic form.

Emergent mode and bound states in single-component one-dimensional lattice fermionic systems

We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.

Modeling superconductivity in the background of a spin-vortex checkerboard

We introduce a microscopic model aimed at describing the behavior of fermionic excitations in the background of a magnetic texture called "spin-vortex checkerboard". This texture was proposed previously as a possible alternative to stripes to interpret the experimental phenomenology of spin and charge modulations in 1/8-doped lanthanum cuprates. The model involves two kinds of interacting fermionic excitations residing in spin-rich and spin-poor regions of the modulated structure. It is a generalization of another model developed earlier for the so-called "grid checkerboard". The principal terms of our model describe the decay of fermionic pairs belonging to spin-poor regions into single fermions occupying spin-rich regions and vice versa. These terms induce intricate fermionic correlations throughout the system but fall short of inducing superconductivity unless arbitrarily small hopping terms are added to the model Hamiltonian. We present the mean-field solution of the model, including, in particular, the temperature dependence of the energy gap. The latter is found to be in a good overall agreement with available experimental data for high-$T_c$ cuprate superconductors.

Strongly magnetized quantum vacuum and ferromagnetic phase transition

AbstractQuantum vacuum in large fields of the order of twice or greater than the critical Schwinger field 2Bc shows strong anisotropic properties: virtual photons as well as electrons and positrons tend to propagate in a parallel direction to the magnetic field. The photon self‐energy acquires an imaginary part, which suggests an instability. In order to overcome this anisotropic behavior, we propose an heuristic model based on fermion pairing of boson‐vacuum n in the form of virtual para‐positronium, a chiral noninvariant electron‐positron bound state leading to a ferromagnetic quantum phase transition of the vacuum for fields of order of twice the critical Schwinger field 2Bc.

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

In a recent work, Murmann et al (2015 Phys. Rev. Lett. 114 080402) have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first calculate Hubbard parameters using the finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single- and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system

Angle-resolved photoemission spectroscopy (ARPES) measures the single-particle excitations of a many-body quantum system with both energy and momentum resolution, providing detailed information about strongly interacting materials. ARPES is a direct probe of fermion pairing, and hence a natural technique to study the development of superconductivity in a variety of experimental systems ranging from high temperature superconductors to unitary Fermi gases. In these systems a remnant gap-like feature persists in the normal state, which is referred to as a pseudogap. A quantitative understanding of pseudogap regimes may elucidate details about the pairing mechanisms that lead to superconductivity, but developing this is difficult in real materials partly because the microscopic Hamiltonian is not known. Here we report on the development of ARPES to study strongly interacting fermions in an optical lattice using a quantum gas microscope. We benchmark the technique by measuring the occupied single-particle spectral function of an attractive Fermi-Hubbard system across the BCS-BEC crossover and comparing to quantum Monte Carlo calculations. We find evidence for a pseudogap in our system that opens well above the expected critical temperature for superfluidity. This technique may also be applied to the doped repulsive Hubbard model which is expected to exhibit a pseudogap at temperatures close to those achieved in recent experiments.

Symmetry-protected spin gaps in quantum wires

This work shows that a strongly correlated phase which is gapped to collective spin excitations but gapless to charge fluctuations emerges as a universal feature in one-dimensional fermionic systems obeying certain symmetries. Namely, nanowires interacting via Coulomb repulsion which are symmetric under time-reversal and spatial inversion symmetry exhibit spin gaps whenever one pair of spin-degenerate subbands is occupied and an arbitrarily weak spin-orbit interaction is present. This general result is independent of the details of the one-dimensional confinement, the fermionic spin or nature of the spin-orbit interaction. In narrow-gap semiconductors, this gap may be of order 10 \textmu eV. This strongly correlated phase may be identified both via an anomalous $h/2e$ flux periodicity in Aharonov-Bohm oscillations and $2e$ periodic Coulomb blockade, features which reflect the existence of fermionic pairing despite the absence of superconductivity and the repulsive nature of the interaction.

Production of an H(h; A) Boson and a Heavy Fermion Pair in Polarized e–e+-Collisions (I)

The production of a Higgs boson H (h; A) and a heavy fermion pair in arbitrarily polarized electron-positron collisions is investigated for the minimal supersymmetric model. The mechanisms of emission of the Higgs boson H (h) by the vector Z0 boson, of the decay of the Z0 boson into the H (h) and A bosons, and of the subsequent production of the heavy fermion pair with further decay of the A and H (h) bosons are studied in detail. Analytical expressions for the differential cross sections and left-right and transverse spin asymmetries are obtained, and dependences of the cross sections and the spin asymmetries on the escape angle and the energy of the Higgs boson A(H;h) are studied. The results are illustrated with graphs.

Forward\u2013backward asymmetry in the gauge-Higgs unification at the International Linear Collider

The signals of the SO(5)times U(1) gauge-Higgs unification model at the International Linear Collider are studied. In this model, Kaluza–Klein modes of the neutral gauge bosons affect fermion pair productions. The deviations of the forward–backward asymmetries of the e^+e^-rightarrow bar{b}b, bar{t}t processes from the standard model predictions are clearly seen by using polarised beams. The deviations of these values are predicted for two cases, the bulk mass parameters of quarks are positive and negative case.

Electroweak one-loop corrections to the process of fermion pair production in electron-positron annihilation

Numerical results for the total cross section, polarization asymmetry, as well as forward-backward asymmetry are presented. Calculations were carried out for longitudinal polarization of the initial electron-positron beams, as well as for the unpolarized case in the one-loop approximation for the standard electroweak Glashow – Weinberg – Salam model without considering quark fields. As a renormalization scheme, we used a non-minimal on-shell scheme with simultaneous renorma lization of the fields. In addition to considering the radiation of soft photons, numerical analysis of hard bremsstrahlung was performed. Analysis of the effect of the cut-off parameters of the phase region of the three-particle final state was made, which are the acollinearity angle between the final leptons, the detecting threshold energies of the final particles, and the radiation energy of the soft photons. An algorithm for obtaining ultraviolet convergent expressions is described. The calculations were carried out in the formalism of the Passarino – Veltman functions in the light-lepton approximation.

Universal thermodynamics of a trapped Fermi gas in the superfluid regime: the role of the Pauli principle

Understanding the universal behavior of strongly-interacting systems of particles has been a major goal in multiple fields of physics from atomic physics to cosmology. Using a recently introduced manybody perturbation formalism for fermions which uses group theoretic and graphical techniques to solve the N-body problem, I study the thermodynamic behavior of the unitary regime for a trapped Fermi gas and investigate the role of the Pauli principle in the emergence of collective behavior, specifically superfluidity at ultralow temperatures. The method, which is called symmetry invariant perturbation theory, has no adjustable parameters and currently offers a solution to the manybody Schrodinger equation through first order in inverse dimensionality exactly. The solution at first order defines collective coordinates in terms of five types of N-body normal modes, identified as symmetric stretch, symmetric bend, single particle angular excitation, single particle radial excitation and phonon. A correspondence is established ‘on paper’ that enforces the Pauli principle through the assignment of specific normal mode quantum numbers. Applied at ultracold temperatures, this normal mode assignment yields occupation only in an extremely low frequency N-body phonon mode. A single particle radial excitation mode at a much higher frequency creates a gap that stabilizes the superfluidity at low temperatures. This radial excitation involves excitation of a single particle out of the synced motion of the phonon mode, rather than the breaking of a fermion pair. Coupled with the corresponding values for the energies at unitarity obtained by this manybody calculation, I obtain good agreement with experimental thermodynamic results. In particular, the lambda transition in the specific heat is clearly seen. Based on these findings, I propose a mechanism for the emergence of superfluidity at ultralow temperatures in this unitary regime that is driven by quantum statistics and the enforcement of the Pauli principle through the selection of normal modes. My results for the calculated thermodynamic quantities suggest that the emergence of some collective behaviors in macroscopic systems is due to the Pauli principle producing manybody pairing and the resulting macroscopic occupation of an N-body phonon mode.

All-in-one relaxion: A unified solution to five particle-physics puzzles

We present a unified relaxion solution to the five major outstanding issues in particle physics: the hierarchy problem, dark matter, matter-antimatter asymmetry, neutrino masses and the strong CP problem. The only additional field content in our construction with respect to standard relaxion models is an up-type vector-like fermion pair and three right-handed neutrinos charged under the relaxion shift symmetry. The observed dark matter abundance is generated automatically by oscillations of the relaxion field that begin once it is misaligned from its original stopping point after reheating. The matter-antimatter asymmetry arises from spontaneous baryogenesis induced by the CPT violation due to the rolling of the relaxion after reheating. The CPT violation is communicated to the baryons and leptons via an operator, $\partial_\mu \phi J^\mu$, where $J^\mu$ consists of right-handed neutrino currents arising naturally from a simple neutrino mass model. Finally, the strong CP problem is solved via the Nelson-Barr mechanism, i.e. by imposing CP as a symmetry of the Lagrangian that is broken only spontaneously by the relaxion. The CP breaking is such that although an ${\cal O}(1)$ strong CKM phase is generated, the induced strong CP phase is much smaller, i.e., within experimental bounds.

The Higgs program and open questions in particle physics and cosmology

The Higgs program is relevant to many of the open fundamental questions in particle physics and cosmology. Thus, when discussing future collider experiments, one way of comparing them is by assessing their potential contributions to progress on these questions. We discuss in detail the capabilities of various proposed experiments in searching for singlet scalars, which are relevant to several of the open questions, and in measuring Higgs decays into fermion pairs, which are relevant to the flavor puzzles. With regard to other interesting questions, we list the most relevant observables within the Higgs program.

Multiple fermions in MoP

Based on the first-principles calculation, we report that the WC-type MoP is a new type of topological semimetal. It can host Weyl semimetal phase with six pairs of Weyl points (WPs) in the first whole Brillouin zone (BZ). In the absence of spin-orbit coupling (SOC), band inversion forms a gapless nodal ring protected by horizontal mirror symmetry [Formula: see text]. The strong SOC in MoP makes the nodal ring fully gapped in the mirror plane, and generates multiple WPs away from the plane. As one hallmark of Weyl semimetals, the unique Fermi arcs are also observed by calculating the projected surface states and Fermi surfaces. Besides the above prodigious features, it also possess an additional four pairs of massless fermions with triply degenerate points (TDPs) in the vicinity of the Fermi level. Each TDP is a band crossing between degenerate and non-degenerate bands along the high-symmetry line in the Brillouin zone, and is protected by crystalline symmetries. Such new type of topological semimetal realizes multiple fermions states and further provides a fancy platform to study emergent physical phenomena.

Searching for boosted dark matter via dark-photon bremsstrahlung

We propose a new search channel for boosted dark matter (BDM) signals coming from the present universe, which are distinct from simple neutrino signals including those coming from the decay or pair-annihilation of dark matter. The signal process is initiated by the scattering of high-energetic BDM off either an electron or a nucleon. If the dark matter is dark-sector U(1)-charged, the scattered BDM may radiate a dark gauge boson (called "dark-strahlung") which subsequently decays to a Standard Model fermion pair. We point out that the existence of this channel may allow for the interpretation that the associated signal stems from BDM, not from the dark-matter-origin neutrinos. Although the dark-strahlung process is generally subleading compared to the lowest-order simple elastic scattering of BDM, we find that the BDM with a significant boost factor may induce an O(10-20%) event rate in the parameter regions unreachable by typical beam-produced dark-matter. We further find that the dark-strahlung channel may even outperform the leading-order channel in the search for BDM, especially when the latter is plagued by substantial background contamination. We argue that cosmogenic BDM searches readily fall in such a case, hence taking full advantage of dark-strahlung. As a practical application, experimental sensitivities expected in the leading-order and dark-strahlung channels are contrasted in dark gauge boson parameter space, under the environment of DUNE far-detectors, revealing usefulness of dark-strahlung.

Few Versus Many-Body Physics of an Impurity Immersed in a Superfluid of Spin 1/2 Attractive Fermions.

In this Letter we investigate the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions and we calculate the beyond-mean-field corrections to the energy of a weakly interacting impurity. We show that these corrections are divergent and have to be regularized by properly accounting for three-body physics in the problem and that our approach naturally provides a unifying framework for Bose and Fermi polaron physics.

Specific heat and pairing of Dirac composite fermions in the half-filled Landau level

A recent proposal argues that an alternate description of the half-filled Landau level is a theory of massless Dirac fermions. We examine the possibility of pairing of these Dirac fermions by numerically solving the coupled Eliashberg equations unlike our previous calculation (Wang and Chakravarty, 2016). In addition, vertex corrections are calculated to be zero from the Ward identity. We find that pairing is possible in non-zero angular momentum channels; only differences are minor numerical shifts. As before, the pairing leads to the gapped Pfaffian and anti-Pfaffian states. However, in our approximation scheme, pairing is not possible in the putative particle–hole symmetric state for ℓ=0 angular momentum. The specific heat at low temperatures of a system of massless Dirac fermions interacting with a transverse gauge field, expected to be relevant for the half-filled Landau level, is calculated. Using the Luttinger formula, it is found to be ∝TlnT in the leading low temperature limit, due to the exchange of transverse gauge bosons. The result agrees with the corresponding one in the nonrelativistic composite fermion theory of Halperin, Lee and Read of the half-filled Landau level.

Scalar democracy

We conjecture that there exists a scalar bound state for every pair of fundamental fermions at a UV (`composite') scale, $\Lambda\gg v_{\text{weak}}$. This implies a large number of universally coupled, sub-critical Higgs doublets. All but the Standard Model Higgs are `dormant,' with large positive squared masses and each receives a small vacuum expectation values via mixing with the Standard Model Higgs. Universal couplings, modulo renormalization group running effects, flips the flavor problem into the masses and mixings of the Higgs system. Doublets associated with heavy fermion masses, $b,c, \tau$ likely lie in the multi-TeV range, but may be observable at the current LHC, or a high-luminosity and/or an energy-upgraded LHC. In the lepton sector we are lead to a Higgs seesaw for neutrino masses, and corollary processes of observable flavor violation. The observation of the first sequential doublet coupled to $\bar{b}b$ with masses $\lesssim 3.5$ TeV would lend credence to the hypothesis.