Fermionic Spin Research Articles

Hidden order in URu2Si2

The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu$_2$Si$_2$. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu$_2$Si$_2$.

Testing the Monte Carlo–mean field approximation in the one-band Hubbard model

The canonical one-band Hubbard model is studied using a computational method that mixes the Monte Carlo procedure with the mean field approximation. This technique allows us to incorporate thermal fluctuations and the development of short-range magnetic order above ordering temperatures, contrary to the crude finite-temperature Hartree-Fock approximation, which incorrectly predicts a N\'eel temperature $T_N$ that grows linearly with the Hubbard $U/t$. The effective model studied here contains quantum and classical degrees of freedom. It thus belongs to the "spin fermion" model family widely employed in other contexts. Using exact diagonalization, supplemented by the traveling cluster approximation, for the fermionic sector, and classical Monte Carlo for the classical fields, the Hubbard $U/t$ vs. temperature $T/t$ phase diagram is studied employing large three and two dimensional clusters. We demonstrate that the method is capable of capturing the formation of local moments in the normal state without long-range order, the non-monotonicity of $T_N$ with increasing $U/t$, the development of gaps and pseudogaps in the density of states, and the two-peak structure in the specific heat. Extensive comparisons with determinant quantum Monte Carlo results suggest that the present approach is qualitatively, and often quantitatively, accurate, particularly at intermediate and high temperatures. Finally, we study the Hubbard model including plaquette diagonal hopping (i.e. the $t-t^\prime$ Hubbard model) in two dimensions and show that our approach allows us to study low temperature properties where determinant quantum Monte Carlo fails due to the fermion sign problem. Future applications of this method include multi-orbital Hubbard models such as those needed for iron-based superconductors.

Representation of quantum field theory in an extended spin space and fermion mass hierarchy

We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries and their representations are determined. Symmetries are flavor or gauge-like, with fixed chirality. After spin 0, 1/2 and 1 fields are obtained in this space, we construct associated interactive gauge-invariant renormalizable terms, showing their equivalence to a Lagrangian formulation, using as example the previously studied (5+1)-dimensional case, with many standard-model connections. At 7+1 dimensions, a pair of Higgs-like scalar Lagrangian is obtained naturally producing mass hierarchy within a fermion flavor doublet.

Diverging nematic susceptibility, physical meaning ofT*scale, and pseudogap in the spin fermion model for the pnictides

Using Monte Carlo simulations with a tunable uniaxial strain, the nematic susceptibility of the spin fermion model for the pnictides is calculated. The results are in excellent agreement with the experiments by Chu et al. [Science 337, 710 (2012)]. Via a Ginzburg-Landau analysis, our study suggests a nematicity in the spin fermion model primarily originating in magnetism, but with the lattice/orbital also playing a key role by boosting up critical temperatures and separating the structural ${T}_{S}$ and N\'eel ${T}_{N}$ transitions. At $T>{T}_{S}$, Curie-Weiss behavior is observed with a characteristic temperature ${T}^{*}$ being the ${T}_{N}$ of the purely electronic system. In this temperature regime, short-range magnetic order with wave vectors $(\ensuremath{\pi},0)\text{\ensuremath{-}}(0,\ensuremath{\pi})$ induce local nematic fluctuations and a density-of-states pseudogap, compatible with several experiments. The present analysis relies on the study of a particular model for the iron superconductors; thus further studies are needed to conclusively establish the driver of nematicity in real materials.

Dark matter in the SO(5) x U(1) gauge-Higgs unification

In the $SO(5) \times U(1)$ gauge-Higgs unification the lightest, neutral component of $n_F$ $SO(5)$-spinor fermions (dark fermions), which are relevant for having the observed unstable Higgs boson, becomes the dark matter of the universe. We show that the relic abundance of the dark matter determined by WMAP and Planck data is reproduced, below the bound placed by the direct detection experiment by LUX, by a model with one light and three heavier ($n_F=4$) dark fermions with the lightest one of a mass from 2.3$\,$TeV to 3.1$\,$TeV. The corresponding Aharonov-Bohm phase $\theta_H$ in the fifth dimension ranges from 0.097 to 0.074. The case of $n_F=3$ ($n_F = 5, 6$) dark fermions yields the relic abundance smaller (larger) than the observed limit.

Formalism of gauge-invariant curvatures and constructing the cubic vertices for massive spin- $$\frac{3}{2}$$ 3 2 field in AdS $$_4$$ 4 space

We study the interaction of massive spin-3/2 field with electromagnetic and gravitational fields in the four dimensional AdS space and construct the corresponding cubic vertices. Construction is based on generalization of Fradkin-Vasiliev formalism, developed for massless higher spin fields, to massive fermionic higher spin fields. The main ingredients of this formalism are the gauge invariant curvatures. We build such curvatures for the massive theory under consideration and show how the cubic vertices are written in their terms.

Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in [formula omitted] space

We construct the frame-like gauge-invariant Lagrangian formulation for massive fermionic arbitrary spin fields in three-dimensional AdS space. The Lagrangian and complete set of gauge transformations are obtained. We also develop the formalism of gauge-invariant curvatures for the massive theory under consideration and show how the Lagrangian is formulated in their terms. The massive spin-5/2 field is discussed as an example.

Chiral anomaly for V-A fields in four- and six-dimensional curved space

The chiral U(1) anomalies associated with a fermion of spin 1/2 interacting with nonabelian vector and axial-vector fields in four- and six-dimensional curved space are given in tensorial form.

Ising quasiparticles and hidden order in URu2Si2

The observation of Ising quasiparticles is a signatory feature of the hidden order phase of . In this paper, we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory, such anisotropic quasiparticles are naturally described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as a symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in .

Effect of vacuum polarization of charged massive fermions in an Aharonov–Bohm field

The effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm (AB) potential in 2+1 dimensions is investigated. The causal Green's function of the Dirac equation with the AB potential is represented via the regular and irregular solutions of the two-dimensional radial Dirac equation. It is shown that the vacuum current density contains the contribution from free filled states of the negative energy continuum as well as that from a bound unfilled state, which can emerge in the above background due to the interaction of the fermion spin magnetic moment with the AB magnetic field while the induced charge density contains only the contribution from the bound state. The expressions for the vacuum charge and induced current densities are obtained (recovered for massless fermions) for the graphene in the field of infinitesimally thin solenoid perpendicular to the plane of a sample. We also find the bound state energy as a function of magnetic flux, fermion spin and the radius of solenoid as well as discuss the role of the so-called self-adjoint extension parameter and determine it in terms of the physics of the problem.

Emergent dome of nematic order around a quantum anomalous Hall critical point

We consider a model of spinful fermions on the triangular lattice which exhibits a C=2 Chern insulator (CI) phase with a quantized anomalous Hall effect, sandwiched between two normal insulator (NI) phases. The first NI-CI quantum phase transition is driven by simultaneous mass inversion of a pair of Dirac fermions, with short range interactions being perturbatively irrelevant. The second CI-NI transition is driven by a single quadratic band touching point protected by momentum space topology and C_6 lattice symmetry. A one-loop renormalization group analysis shows that short range interactions lead to a single marginally relevant perturbation at this transition. We obtain the mean field phase diagram of this model incorporating weak repulsive Hubbard interactions, finding an emergent nematic dome around this CI-NI topological phase transition. We discuss the crossovers in the anomalous Hall conductivity at nonzero temperature, and the Landau theory of the quantum and thermal transitions out of the nematic phase. Our results may be relevant to ferromagnetic double perovskite films with spin-orbit coupling which have been proposed to host such a NI-CI transition. Our work provides perhaps the simplest example of an emergent phase near a quantum phase transition.

Spin fluctuation and Fermi surface instability in ferromagnetic superconductors

Abstract We review the ferromagnetic superconductivity observed in the uranium based compounds, namely UGe2, URhGe and UCoGe, where the spin-triplet state is most likely realized. An unusual upper critical field H c2 , which is enhanced under a magnetic field in a certain field direction, is discussed in terms of spin fluctuations and of Fermi surface instabilities.

Prospects for electron spin-dependent short-range force experiments with rare earth iron garnet test masses

A study of the possible interactions between fermions assuming only rotational invariance has revealed 15 forms for the potential involving the fermion spins. We review the experimental constraints on unobserved macroscopic, spin-dependent interactions between electrons in the range below 1 cm. An existing experiment, using 1 kHz mechanical oscillators as test masses, has been used to constrain mass-coupled forces in this range. With suitable modifications, including spin-polarized test masses, this experiment can be used to explore all 15 possible spin-dependent interactions between electrons in this range with unprecedented sensitivity. Samples of ferrimagnetic dysprosium iron garnet have been fabricated in the suitable test mass geometry and shown to have high spin density with very low intrinsic magnetism.

Global Well‐Posedness of the Spatially Homogeneous Hubbard‐Boltzmann Equation

The Hubbard model is a simplified description for the evolution of interacting spin fermions on a d‐dimensional lattice. In a kinetic scaling limit, the Hubbard model can be associated with a matrix‐valued Boltzmann equation, the Hubbard‐Boltzmann equation. Its collision operator is a sum of two qualitatively different terms: The first term is similar to the collision operator of the fermionic Boltzmann‐Nordheim equation. The second term leads to a momentum‐dependent rotation of the spin basis. The rotation is determined by a principal value integral that depends quadratically on the state of the system and might become singular for nonsmooth states. In this paper, we prove that the spatially homogeneous equation nevertheless has global solutions in for any initial data W0 that satisfies the “Fermi constraint” in the sense that 0 ≤ W0 ≤ 1 almost everywhere. We also prove that there is a unique “physical” solution for which the Fermi constraint holds at all times. For the proof, we need to make a number of assumptions about the lattice dispersion relation which, however, are satisfied by the nearest‐neighbor Hubbard model provided that d ≥ 3. These assumptions suffice to guarantee that, although possibly singular, the local rotation term is generated by a function in .© 2015 Wiley Periodicals, Inc.

Kinetic equations for massive Dirac fermions in electromagnetic field with non-Abelian Berry phase

We derive a semiclassical effective action and the kinetic equation for massive Dirac fermions in electromagnetic fields. The non-Abelian Berry phase structure emerges from two helicity states of massive fermions with positive energy. The classical spin emerges as a vector in SU(2) helicity space. The continuity equations for the fermion number and the classical spin are derived. The fermion number is conserved while the spin charge is not conserved by anomaly. Previous results about the coefficients of the chiral magnetic effect for the fermion and axial currents in the chiral limit can be reproduced after including the antifermion contributions. This provides an example for the emerging spin and non-Abelian Berry phase of Dirac fermions arising from the fermion mass.

Three interacting atoms in a one-dimensional trap: a benchmark system for computational approaches

We provide an accurate calculation of the energy spectrum of three atoms interacting through a contact force in a one-dimensional harmonic trap, considering both spinful fermions and spinless bosons. We use fermionic energies as a benchmark for the exact-diagonalization technique (also known as full configuration interaction), which is found to slowly converge in the case of strong inter-atomic attraction.

Bound states of massive fermions in Aharonov–Bohm-like fields

Bound states of massive fermions in Aharonov–Bohm (AB)-like fields have analytically been studied. The Hamiltonians with the (AB)-like potentials are essentially singular and therefore require specification of a one-parameter self-adjoint extension. We construct self-adjoint Dirac Hamiltonians with the AB potential in 2+1 dimensions that are specified by boundary conditions at the origin. It is of interest that for some range of the extension parameter the AB potential can bind relativistic charged massive fermions. The bound-state energy is determined by the AB magnetic flux and depends upon the fermion spin and extension parameter; it is a periodical function of the magnetic flux. We also construct self-adjoint Hamiltonians for the so-called Aharonov–Casher (AC) problem, show that nonrelativistic neutral massive fermions can be bound by the (AC) background, determine the range of the extension parameter in which fermion bound states exist, and find their energies as well as wave functions.

Searches for possible T-odd and P-odd short range interactions using polarized nuclei

Various theories predict the possible existence of T-odd and P-odd shortrange forces between spin ½ fermions, proportional to S・r where S is the fermion spin and r is the separation between particles. We use ensembles of polarized nuclei and an un-polarized mass to search for such a force over sub-mm ranges. We established an improved upper bound on the product gsgpn of the scalar coupling to particles in the un-polarized mass and the pseudo-scalar coupling of polarized neutrons for force ranges from 10−4 to 10−2 m, corresponding to a mass range of 2・10−3 to 2・10−5 eV for the exchange boson [1].

Competing effective interactions of Dirac electrons in the Spin–Fermion system

Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin–Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu–Jona-Lasinio-like, excitonic term and a spin–spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants.

The Pauli Exclusion Principle. Can It Be Proved?

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the Pauli exclusion principle, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrodinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory.