Fermionic Spin Research Articles

Many-Body Entanglement in Short-Range Interacting Fermi Gases for Metrology.

We explore many-body entanglement in spinful Fermi gases with short-range interactions, for metrology purposes. We characterize the emerging quantum phases via density-matrix renormalization group simulations and quantify their entanglement content for metrological usability via quantum Fisher information (QFI). Our study establishes a method, promoting QFI to be an order parameter. Short-range interactions reveal to build up metrologically promising entanglement in the XY-ferromagnetic and cluster ordering, the cluster physics being unexplored so far.

Lagrangian formulation for the infinite spin N = 1 supermultiplets in d = 4

We provide an explicit Lagrangian construction for the massless infinite spin N=1 supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.

Scalar-fermion analytic bootstrap in 4D

In this work we discuss an analytic bootstrap approach [1, 2] in the context of spinning 4D conformal blocks [3, 4]. As an example we study the simplest spinning case, the scalar-fermion correlator leftlangle phi psi phi overline{psi}rightrangle . We find that to every pair of primary scalar ϕ and fermion ψ correspond two infinite towers of fermionic large spin primary operators. We compute their twists and products of OPE coefficients using both s-t and u-t bootstrap equations to the leading and sub-leading orders. We find that the leading order is represented by the scalar-fermion generalized free theory and the sub-leading order is governed by the minimal twist bosonic (light scalars, currents and the energy-momentum tensor) and fermionic (light fermions and the suppersymmetric current) operators present in the spectrum.

Strong Spin–Charge Coupling and Its Manifestation in the Quasiparticle Structure, Cooper Instability, and Electromagnetic Properties of Cuprates

The Fermi excitation spectrum, the problem of Cooper instability, and the Londons magnetic field penetration depth in cuprate superconductors are considered using the unified conception based on accounting for the strong coupling between the spin of copper ions and holes at oxygen ions. This coupling leads to strong renormalization of the primary spectrum of oxygen holes with the formation of spin-polaron quasiparticles. Analysis of Cooper instability performed using the spin-polaron concept for different channels has shown that only the superconducting d-wave pairing occurs in the ensemble of spin-polaron quasiparticles, and there are no solutions corresponding to the s-wave pairing. It has been demonstrated that the superconducting d-wave pairing is not suppressed by the Coulomb repulsion of holes located at neighboring oxygen ions. This effect is due to peculiarities in the crystallographic structure of the CuO2 plane and the aforementioned strong spin–fermion coupling. As a result, such interaction of holes is omitted in the kernel of the integral equation for the superconducting order parameter with the d-wave symmetry. It has been shown the Hubbard repulsion of holes and their interaction for the second coordination sphere of the oxygen sublattice for actual intensities of the interaction do not suppress the d-wave type of superconductivity. For the spin-polaron ensemble, we have analyzed the dependence of the Londons magnetic field penetration depth on the temperature and hole concentration. It has been established that the peculiarities of this dependence are closely related to specific features of the spin-polaron spectrum.

Density-wave steady-state phase of dissipative ultracold fermions with nearest-neighbor interactions

In this work we investigate the effect of local dissipation on the presence of density-wave ordering in spinful fermions with both local and nearest-neighbor interactions as described by the extended Hubbard model. We find density-wave order to be robust against decoherence effects up to a critical point where the system becomes homogeneous with no spatial ordering. Our results will be relevant for future cold-atom experiments using fermions with non-local interactions arising from the dressing by highly-excited Rydberg states, which have finite lifetimes due to spontaneous emission processes.

The massive Dirac equation in the Kerr-Newman-de Sitter and Kerr-Newman black hole spacetimes

Exact solutions of the Dirac general relativistic equation that describe the dynamics of a massive, electrically charged particle with half-integer spin in the curved spacetime geometry of an electrically charged, rotating Kerr-Newman-(anti) de Sitter black hole are investigated. We first, derive the Dirac equation in the Kerr-Newman-de Sitter (KNdS) black hole background using a generalised Kinnersley null tetrad in the Newman-Penrose formalism. Subsequently in this frame and in the KNdS black hole spacetime, we prove the separation of the Dirac equation into ordinary differential equations for the radial and angular parts. Under specific transformations of the independent and dependent variables we prove that the transformed radial equation for a massive charged spin fermion in the background KNdS black hole constitutes a highly non-trivial generalisation of Heun’s equation since it possess five regular finite singular points. Using a Regge-Wheeler-like independent variable we transform the radial equation in the KNdS background into a Schrödinger like differential equation and investigate its asymptotic behaviour near the event and cosmological horizons. For the case of a massive fermion in the background of a Kerr-Newman (KN) black hole we first prove that the radial and angular equations that result from the separation of Dirac’s equation reduce to the generalised Heun differential equation (GHE). The local solutions of such GHE are derived and can be described by holomorphic functions whose power series coefficients are determined by a four-term recurrence relation. In addition using asymptotic analysis we derive the solutions for the massive fermion far away from the KN black hole and the solutions near the event horizon . The determination of the separation constant as an eigenvalue problem in the KN background is investigated. Using the aforementioned four-term recursion formula we prove that in the non-extreme KN geometry there are no bound states with , where ω and μ are the energy and mass of the fermion respectively.

Jordan\u2013Wigner transformations for tree structures

The celebrated Jordan–Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin–fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.

Metallic spin-liquid-like behavior of LiV2O4

LiV$_2$O$_4$ spinel is known to exhibit heavy fermion-like behavior below a characteristic temperature $T_K\simeq 20$ K, while it preserves a paramagnetic state down to $T\sim10^{-2}$ K due to geometrical frustration. Here, it is shown that the dynamical spin susceptibility $\chi({\bf q},\omega)$ in LiV$_2$O$_4$ exhibits anomalous duality which is modeled as a sum of itinerant ($\chi_{\rm F}$) and local ($\chi_{\rm L}$) components,and that the local spin dynamics inferred from $\chi_{\rm L}({\bf q},\omega)$ is qualitatively different from that expected from time-averaged bulk properties. The anomaly coexists with the marginal Fermi liquid behavior inferred from the $-\ln T$ dependence of the electronic specific heat over a wide temperature range below $T_K$. We argue that such unusual properties of LiV$_2$O$_4$ can be attributed to the putative metallic spin liquid state emerging near the quantum critical point between spin glass and Fermi liquid states.

Spin-charge separation effects in the low-temperature transport of one-dimensional Fermi gases

We study the transport properties of a one-dimensional spinful Fermi gas, after junction of two semi-infinite sub-systems held at different temperatures. The ensuing dynamics is studied by analysing the space-time profiles of local observables emerging at large distances $x$ and times $t$, as a function of $\zeta = x/t$. At equilibrium, the system displays two distinct species of quasi-particles, naturally associated with different physical degrees of freedom. By employing the generalised hy- drodynamic approach, we show that when the temperatures are finite no notion of separation can be attributed to the quasi-particles. In this case the profiles can not be qualitatively distinguished by those associated to quasi-particles of a single species that can form bound states. On the contrary, signatures of separation emerge in the low-temperature regime, where two distinct characteristic ve- locities appear. In this regime, we analytically show that the profiles display a piece-wise constant form and can be understood in terms of two decoupled Luttinger liquids.

Microwave preparation of two-dimensional fermionic spin mixtures

We present a method for preparing a single two-dimensional sample of a two-spin mixture of fermionic potassium in a single antinode of an optical lattice, in a quantum-gas microscope apparatus. Our technique relies on spatially-selective microwave transitions in a magnetic field gradient. Adiabatic transfer pulses were optimized for high efficiency and minimal atom loss and heating due to spin-changing collisions. We have measured the dynamics of those loss processes, which are more pronounced in the presence of a spin mixture. As the efficient preparation of atoms in a single antinode requires a homogeneous transverse magnetic field, we developed a method to image and minimize the magnetic field gradients in the focal plane of the microscope.

Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes

The local free action principle for bosonic unconstrained higher spin gauge fields in $d$-dimensional (A)dS$_d$ spacetime has been already established by Segal. However, later on, Schuster and Toro, in 4-dimensional flat spacetime, extracted such an action from their bosonic continuous spin gauge theory, when the continuous spin parameter vanishes. On the other hand, similar to the Schuster-Toro's action, we found the fermionic continuous spin gauge theory in 4-dimensional flat spacetime. Thus it is noteworthy to take out its fermionic higher spin formulation in a limit, and generalize it to $d$-dimensional (A)dS$_d$ spacetime. Therefore, in this paper, we will present a similar action principle \`a la Segal for fermions in $d$-dimensional (A)dS$_d$ spacetime. Moreover, at the level of equations of motion, we will demonstrate how the Fronsdal and the Fang-Fronsdal equations in $d$-dimensional (A)dS$_d$ spacetime are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic higher spin actions mentioned above.

Spin-orbit coupling and topological states in an F=32 cold Fermi gas

In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin $F>\tfrac{1}{2}$, if the optical potential is properly designed, and spin-orbit coupling is relevant. The latter is shown to be induced by letting the fermions interact with a specially tuned arrangement of polarized laser beams. When the system is subject to a perpendicular magnetic field, time reversal symmetry is broken but the ensuing Hamiltonian is still endowed with a mirror symmetry. Topological insulators for fermions of higher spins are fundamentally distinct from those pertaining to spin $\frac{1}{2}$. The underlying physics reveals a plethora of positive and negative mirror Chern numbers, respectively corresponding to chiral and anti-chiral edge states. Here, for simplicity, we concentrate on the case $F=\tfrac{3}{2}$ (which is suitable for $^{6}$Li or $^2$H atoms) but extension to higher spins (such as $^{40}$K whose ground-state spin is $F=\tfrac{9}{2}$), is straightforward.

Interpolating quantum electrodynamics between instant and front forms

The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter $\delta$ spanning between the instant form dynamics (IFD) at $\delta =0$ and the front form dynamics which is now known as the light-front dynamics (LFD) at $\delta =\pi/4$. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous contribution to the fermion propagator, which is genuinely distinguished from the ordinary equal-time forward and backward propagation of relativistic fermion degrees of freedom. As discussed in our previous work, the helicity of the on-mass-shell fermion spinors in LFD is also distinguished from the ordinary Jacob-Wick helicity in the IFD with respect to whether the helicity depends on the reference frame or not. To exemplify the characteristic difference of the fermion propagator between IFD and LFD, we compute the helicity amplitudes of typical QED processes such as $e^+ e^- \to \gamma \gamma$ and $e \gamma \to e \gamma$ and present the whole landscape of the scattering amplitudes in terms of the frame dependence or the scattering angle dependence with respect to the interpolating angle dependence. Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the infinite momentum frame approach and the LFD.

Anesthetic Action and "Quantum Consciousness": A Match Made in Olive Oil.

Anesthetic Action and "Quantum Consciousness": A Match Made in Olive Oil.

Entanglement in a fermionic spin chain containing a single mobile boson under decoherence

The concurrence between first and the last sites of a fermionic spin chain containing a single boson is rigorously investigated at finite low temperature in the vicinity of a weak homogeneous magnetic field. We consider the boson as a mobile spin-1 particle through the chain and study concurrence without/under decoherence and express some interesting phase flip and bit flip reactions of the pairwise entanglement between first and the last half-spins in the chain. Our investigations show that the concurrence between two considered half-spins has different behavior for various positions of the single boson along the chain. Indeed, we realize that the single boson mobility has an essential role to probe the pairwise entanglement intensity between two spins located at the opposite ends of a fermionic chain. Interestingly, the entanglement remains alive for higher temperatures when the boson is the nearest neighbor of the first fermion. When the boson is at the middle of chain, it is demonstrated that the threshold temperature (at which the concurrence vanishes) versus decoherence rate can be considered as a threshold temperature boundary. These results pave the way to set and interpret the numerical and analytical expressions for utilizing quantum information in realistic scenarios such as quantum state transmission, quantum communication science and quantum information processing, where the both fermion-fermion and fermion-boson correlations should be taken in to account.

Quantum States of a Neutral Massive Fermion with an Anomalous Magnetic Moment in an External Electric Field

The quantum dynamics of a nonrelativistic neutral massive fermion with an anomalous magnetic moment (AMM) is examined in the external electric field of an infinitely long thin homogeneously charged thread in the plane with a normal directed along the thread. The Hamiltonian of the Dirac–Pauli equation for a neutral fermion with AMM is essentially singular in the considered external field and requires a supplementary extension of the definition in order for it to be treated as a self-adjoint quantum-mechanical operator. All one-parameter self-adjoint extensions of the Hamiltonian of the Dirac–Pauli equation in the considered external field are found in the nonrelativistic approximation. The corresponding Hilbert space of squareintegrable functions, including a singularity point of the Hamiltonian, is specified for each self-adjoint extension of the Hamiltonian. The wave functions of free and bound states, as well as discrete energy levels, are determined by the self-adjoint extension method and their correspondence with similar quantities obtained by the physical regularization procedure is discussed. It is shown that energy levels of bound states are simple poles of the scattering amplitude, which should be extended in definition by introducing the self-adjoint extension parameter into it. Expressions for the scattering amplitude and cross-section, depending on the orientation of the initial-state spin of fermion, are obtained.

Quantum phases of spinful Fermi gases in optical cavities

We explore the quantum phases emerging from the interplay between spin and motional degrees of freedom of a one-dimensional quantum fluid of spinful fermionic atoms, effectively interacting via a photon-mediating mechanism with tunable sign and strength g, as it can be realized in present-day experiments with optical cavities. We find the emergence, in the very same system, of spin- and atomic-density wave ordering, accompanied by the occurrence of superfluidity for g > 0, while cavity photons are seen to drive strong correlations at all g values, with fermionic character for g > 0, and bosonic character for g < 0. Due to the long-range nature of interactions, to infer these results we combine mean-field and exact diagonalization methods supported by bosonization analysis.

Canonical quantization of the covariant fields on de Sitter space–times

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

Gauge anomaly with vector and axial-vector fields in 6D curved space

Imposing the conservation equation of the vector current for a fermion of spin $\frac{1}{2}$ at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial--vector fields in six--dimensional curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial--vector field is Abelian.

Quasiclassical Theory of Spin Dynamics in Superfluid $$^3$$ 3 He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States

We develop a theory based on the formalism of quasiclassical Green's functions to study the spin dynamics in superfluid $^3$He. First, we derive kinetic equations for the spin-dependent distribution function in the bulk superfluid reproducing the results obtained earlier without quasiclassical approximation. Then we consider a spin dynamics near the surface of fully gapped $^3$He-B phase taking into account spin relaxation due to the transitions in the spectrum of localized fermionic states. The lifetime of longitudinal and transverse spin waves is calculate taking into account the Fermi-liquid corrections which lead to the crucial modification of fermionic spectrum and spin responses.