Fermionic Spin Research Articles

Spin–orbit enabled unconventional Stoner magnetism

The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This instability captures the interplay of Coulomb repulsion, Pauli exclusion, and twofold fermionic spin degeneracy. In materials with spin–orbit coupling, this fermionic spin is generalized to a twofold degenerate pseudospin which is typically believed to have symmetry properties as spin. Here, we identify a distinct symmetry of this pseudospin that forbids it to couple to a Zeeman field. This “spinless” property is required to exist in five nonsymmorphic space groups and has nontrivial implications for superconductivity and magnetism. With Coulomb repulsion, Fermi surfaces composed primarily of this spinless pseudospin property give rise to Stoner instabilities into magnetic states that are qualitatively different than ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, are noncollinear, and exhibit momentum-dependent energy band spin-splittings. In superconductors, for all pairing symmetries and field orientations, this spinless pseudospin extinguishes paramagnetic limiting. We discuss applications to superconducting UCoGe and magnetic NiS 2 − x Se x .

Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, QN, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from QN is given by χ−1∝|Δq|. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ−1∝|Δq|2 dependence yields a robust finite-T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the (t−t′) Hubbard model and found that at large U/t>5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ−1∝|Δq|2. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024

Adiabatic gauge potential and integrability breaking with free fermions

We revisit the problem of integrability breaking in free fermionic quantum spin chains. We investigate the so-called adiabatic gauge potential (AGP), which was recently proposed as an accurate probe of quantum chaos. We also study the so-called weak integrability breaking, which occurs if the dynamical effects of the perturbation do not appear at leading order in the perturbing parameter. A recent statement in the literature claimed that integrability breaking should generally lead to an exponential growth of the AGP norm with respect to the volume. However, afterwards it was found that weak integrability breaking is a counter-example, leading to a cross-over between polynomial and exponential growth. Here we show that in free fermionic systems the AGP norm always grows polynomially, if the perturbation is local with respect to the fermions, even if the perturbation strongly breaks integrability. As a by-product of our computations we also find, that in free fermionic spin chains there are operators which weakly break integrability, but which are not associated with known long range deformations.

Jordan–Wigner transformation constructed for spinful fermions at S=1/2 spins in one dimension

ABSTRACT 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.

EPR Correlations Using Quaternion Spin

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 12—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 12, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q8, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox.

Massive propagating modes of torsion

The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De Donder–Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the Riemann–Cartan tensor. Since the latter adds the derivative of torsion to the equations of motion, torsion is no longer identical to spin density, as in the Einstein–Cartan theory, but an additional propagating degree of freedom. As torsion turns out to be totally anti-symmetric, it can be parametrised via a single axial vector. It is shown in this paper that, in the weak torsion limit, the axial vector obeys a wave equation with an effective mass term which is partially dependent on the scalar curvature. The source of torsion is thereby given by the fermion axial current which is the net fermionic spin density of the system. Possible measurable effects and approaches to experimental analysis are addressed. For example, neutron star mergers could act as a dipoles or quadrupoles for torsional radiation, and an analysis of radiation of pulsars could lead to a detection of torsion wave background radiation.

Anomalies and persistent order in the chiral Gross-Neveu model

We study the 2d chiral Gross-Neveu model at finite temperature T and chemical potential μ. The analysis is performed by relating the theory to a SU(N) × U(1) Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At μ = 0 we show that a certain ℤ2-valued ’t Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any N and any T > 0. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for T > 0 of the inhomogeneous chiral phase configuration found at T = 0 for any N and any μ. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for T > 0 and any μ for periodic fermions, as expected from anomaly considerations. A large N analysis confirms the above findings.

Majorana fermions in a two-band two-dimensional Fermi system

Majorana fermions represent potential candidates for realizing fault-tolerant topological quantum computation. We obtain the exact mapping between a two-band hybridized model and a model with a topological superconducting state supporting Majorana fermions. The antisymmetric hybridization employed resembles that of spin–orbit coupling. We consider the situation where the model Hamiltonian comprises only inter-band s-wave pairing, i.e. the one in which the superconducting pairing is formed by one fermion from one of the bands and another fermion of opposite spin and momentum from the other band. From this we obtain an effective Hamiltonian of the px+ipy superconductor and calculate the topological invariant that distinguishes the weak and strong pairing phases. We also obtain the gap parameter and chemical potential of the Fermi system under spin–orbit coupling beyond the mean-field approximation. We show that the spin–orbit coupling substantially enhances the density of states at the Fermi surface.

Resonant inelastic X-ray scattering applications in quantum materials

The essence of quantum materials lies in the intricate coupling among charge, spin, orbital and lattice degrees of freedom. Although X-ray photoemission spectroscopy and inelastic neutron scattering have advantages in detecting fermionic single-particle spectral function and bosonic spin excitations in quantum materials, respectively, probing other bosonic collective excitations especially their coupling is not possible until the establishment of the advanced resonant inelastic X-ray scattering (RIXS). In the past decades, RIXS has flourished with continuously improved energy resolution which made a paradigm shift from measuring crystal-field splitting and the charge-transfer excitation, to probing collective excitations and the order parameters of all degrees of freedom. This review paper summarises the latest research progress of quantum materials studied by the soft X-ray RIXS. For instance, three-dimensional collective charge excitations, plasmons, were discovered experimentally by RIXS in both electron and hole doped cuprate superconductors. The collective orbital excitations and excitons were found in copper and nickel based quantum materials. For the newly discovered nickelate superconductors, RIXS has made substantial contributions to characterising their electronic and magnetic excitations and the related ordering phenomena critical for an in-depth understanding of the underlying superconducting mechanicsm. The RIXS is a unique tool in probing the higher-order spin excitations in quantum materials due to the strong spin-orbit coupling and the core-valence exchange interaction. The RIXS is also found to be superior in probing the Stoner magnetic excitations in magnetic metals and topological magnetic materials. Finally, the development of RIXS technology in Chinese large-scale research facilities is briefly prospected.

Error-mitigated quantum simulation of interacting fermions with trapped ions

Quantum error mitigation has been extensively explored to increase the accuracy of the quantum circuits in noisy-intermediate-scale-quantum (NISQ) computation, where quantum error correction requiring additional quantum resources is not adopted. Among various error-mitigation schemes, probabilistic error cancellation (PEC) has been proposed as a general and systematic protocol that can be applied to numerous hardware platforms and quantum algorithms. However, PEC has only been tested in two-qubit systems and a superconducting multi-qubit system by learning a sparse error model. Here, we benchmark PEC using up to four trapped-ion qubits. For the benchmark, we simulate the dynamics of interacting fermions with or without spins by applying multiple Trotter steps. By tomographically reconstructing the error model and incorporating other mitigation methods such as positive probability and symmetry constraints, we are able to increase the fidelity of simulation and faithfully observe the dynamics of the Fermi–Hubbard model, including the different behavior of charge and spin of fermions. Our demonstrations can be an essential step for further extending systematic error-mitigation schemes toward practical quantum advantages.

Exchange energies and density functionals for systems of fermions of arbitrary spin

Exchange energies and density functionals for systems of fermions of arbitrary spin

Hadronic Isospin Helicity and the Consequent SU(4) Gauge Theory

A new approach to the Dirac equation and the associated hadronic symmetries is proposed. In this approach, we linearize the second Casimir operator of the Lorentz Group, which is defined by the energy–momentum four-vector and the fermion spin, thereby using the spinor-helicity representation instead of the three-vector representation of the particle momentum and spin vector. We then expand the so-obtained standard Dirac equation by employing an inner abstract “hadronic” isospin, initially describing a SU(2) fermion doublet. Application of the spin-helicity representation of that isospin leads to the occurrence of a quadruplet of inner states, revealing the SU(4) symmetry via the isospin helicity operator. This further leads to two independent fermion state spaces, specifically, singlet and triplet states, which we interpret as U(1) symmetry of the leptons and SU(3) symmetry of the three quarks, respectively. These results indicate the genuinely very different physical nature of the strong SU(4) symmetry in comparison to the chiral SU(2) symmetry. While our approach does not require the a priori concept of grand unification, such a notion arises naturally from the formulation with the isospin helicity. We then apply the powerful procedures developed for the electroweak interactions in the SM, in order to break the SU(4) symmetry by means of the Higgs mechanism involving a scalar Higgs field as an SU(4) quadruplet. Its finite vacuum creates the masses of the three vector bosons involved, which can change the three quarks into a lepton and vice versa. Finally, we consider a toy model for calculation of the strong coupling constant of a Yukawa potential.

Spin and valley-polarized multiple Fermi surfaces of α -RuCl3/bilayer graphene heterostructure

We report the transport properties of α-RuCl3/bilayer graphene heterostructures, where carrier doping is induced by a work function difference, resulting in distinct electron and hole populations in α-RuCl3 and bilayer graphene, respectively. Through a comprehensive analysis of multi-channel transport signatures, including Hall measurements and quantum oscillation, we unveil significant band modifications within the system. In particular, we observe the emergence of spin and valley-polarized multiple hole-type Fermi pockets, originating from the spin-selective band hybridization between α-RuCl3 and bilayer graphene, breaking the spin degree of freedom. Unlike the α-RuCl3/monolayer graphene system, the presence of different hybridization strengths between α-RuCl3 and the top and bottom graphene layers leads to an asymmetric behavior of the two layers, confirmed by effective mass experiments, resulting in the manifestation of valley-polarized Fermi pockets. These compelling findings establish α-RuCl3 proximitized to bilayer graphene as an outstanding platform for engineering its unique low-energy band structure.

On massive higher spin supermultiplets in d = 3

In this paper, using a frame-like gauge invariant formulation of the massive higher spin bosons and fermions, we develop a direct construction of the completely off-shell cubic vertices describing an interaction of the massless gravitino with the massive higher spin supermultiplets. To achieve the invariance under the local supersymmetry we introduce all necessary supertransformations (both for the physical as well as for the auxiliary fields) and thus all the supercurrents constructed are conserved on-shell. As an illustration of the technique used we present some lower superspin examples and then we consider the arbitrary superspin. We also check that the whole construction is completely consistent with all bosonic and fermionic gauge symmetries of the fields entering the supermultiplets.

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot.

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Tuning the spin of Dirac fermions on the surface of topological insulators in proximity to a helical spin density wave

We investigate the spin tunability of Dirac fermions on the surface of a 3D topological insulator in proximity to a helical spin density wave, acting as an applied one-dimensional periodic potential for spins produced by spiral multiferroic oxide. It is observed that the spin mean values of Dirac fermion undergo oscillations under the influence of such a periodic potential created by the exchange field of magnetization. The tunability of spin is strongly affected by the strength, orientation and period of the exchange field. In particular, the mean values of spin are anisotropic around the Dirac point, depending strongly on the amplitude and spatial period of the periodic potential. We also find that the spin expectation values change significantly by changing the plane of magnetization. Interestingly, the in-plane components of spin mean values perform pronounced oscillations, whereas the out of plane component does not oscillate at all. The oscillations of planar components of spin are originated from the spin-momentum locking on the surface of topological insulator.

Spin‐Decoupling and In‐Situ Nuclear Magnetometer with Hyperpolarized Nuclear Spin

AbstractThis paper investigates the dynamical properties of the spin‐coupling ensemble, with a focus on the spin‐decoupling phenomenon. The nuclear spin in such systems is significantly impacted by the electron spin when the main magnetic field approaches the Fermi contact field of nuclear spin, leading to measurement inaccuracies. A comprehensive dynamics model of the electron‐nuclear spin coupling ensemble has been established and analyzed. It proposes that the primary magnetic field augmenting effectively disentangles the precession frequency of the two spin‐coupling species, thereby yielding a spin‐decoupled state. Such a state allows nuclear spin serves as a high sensitive element for magnetic field measurements, while electron spin serves as a probe to acquire the precession of nuclear spin. With proposed method, a magnetic field resolution of 0.75 nT in a 12000 nT environment is achieved, indicating potential for magnetic field detection in geomagnetic environments. It further demonstrates measurements of electron spin Fermi contact interaction and polarization based on spin‐decoupling and in situ nuclear spin precession, results indicate measurement errors close to 1%. These results demonstrate the effectiveness of our approach in improving the accuracy and sensitivity of magnetic field measurements in spin‐coupled systems such as co‐magnetometers, nuclear magnetic resonance gyroscopes, and nuclear magnetometers.

The dark Stodolsky effect: constraining effective dark matter operators with spin-dependent interactions

We present a comprehensive discussion of the Stodolsky effect for dark matter (DM), and discuss two techniques to measure the effect and constrain the DM parameter space. The Stodolsky effect is the spin-dependent shift in the energy of a Standard Model (SM) fermion sitting in a bath of neutrinos. This effect, which scales linearly in the effective coupling, manifests as a small torque on the SM fermion spin and has historically been proposed as a method of detecting the cosmic neutrino background. We generalise this effect to DM, and give expressions for the induced energy shifts for DM candidates from spin-0 to spin-3/2, considering all effective operators up to mass dimension-6. In all cases, the effect scales inversely with the DM mass, but requires an asymmetric background. We show that a torsion balance experiment is sensitive to energy shifts of ΔE ≳ 10-28 eV, whilst a more intricate setup using a SQUID magnetometer is sensitive to shifts of ΔE ≳ 10-32 eV. Finally, we compute the energy shifts for a model of scalar DM, and demonstrate that the Stodolsky effect can be used to constrain regions of parameter space that are not presently excluded.

Ising analogs of quantum spin chains with multispin interactions

A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains---but with inhomogeneous couplings---which have the same spectra as the novel spin chains with multispin interactions. The Ising models are obtained by associating an antisymmetric tridiagonal matrix to the polynomials that characterize the quasienergies of the system via a modified Euclidean algorithm. For the simplest nontrivial case, corresponding to the Fendley model, the phase diagram of the inhomogeneous Ising model is investigated numerically. It is characterized by gapped phases separated by critical lines with order-disorder transitions depending on the parity of the total number of energy density operators in the Hamiltonian.

Towards a direct detection of the spin of dark matter

We investigate the contribution of higher spin particles in the signal of direct detection searches for dark matter. We consider a bosonic or fermionic higher spin dark matter (HSDM) candidate which interacts with the Standard Model via a dark U(1) mediator. For a particular subclass of interactions, spin-polarized targets may be used for spin determination: The angular dependence of scatterings can distinguish integer (spin-s) vs. half-integer (spin-s+1/2), while the recoil energy dependence of the signal determines s. We consider also the signal of a supersymmetric higher spin dark sector, which suggests a characteristic signal (“SUSY Rilles”) for directional direct detection.