Dynamical Fermions Research Articles

Capturing the transformation

Quantum Gases Quantum statistics dictates the behavior of identical particles in the quantum world: Bosons like to congregate, whereas fermions avoid one another. However, strong interactions can cause a string of bosons to behave like fermions. This so-called fermionization phenomenon has been studied in equilibrium. Wilson et al. instead focused on dynamical fermionization in a nonequilibrium system consisting of tubes of strongly interacting bosonic rubidium atoms. After letting the tubes expand in the axial direction, the researchers monitored the momentum distribution of the atoms and found that it evolved from bosonic-like to fermionic-like. Science , this issue p. [1461][1] [1]: /lookup/doi/10.1126/science.aaz0242

Observation of dynamical fermionization.

The wave function of a Tonks-Girardeau (T-G) gas of strongly interacting bosons in one dimension maps onto the absolute value of the wave function of a noninteracting Fermi gas. Although this fermionization makes many aspects of the two gases identical, their equilibrium momentum distributions are quite different. We observed dynamical fermionization, where the momentum distribution of a T-G gas evolves from bosonic to fermionic after its axial confinement is removed. The asymptotic momentum distribution after expansion in one dimension is the distribution of rapidities, which are the conserved quantities associated with many-body integrable systems. Our measurements agree well with T-G gas theory. We also studied momentum evolution after the trap depth is suddenly changed to a new nonzero value, and we observed the theoretically predicted bosonic-fermionic oscillations.

Nucleon mass and isovector couplings in 2+1 -flavor dynamical domain-wall lattice QCD near physical mass

We report nucleon mass, isovector vector and axial-vector charges, and tensor and scalar couplings, calculated using two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD collaborations. These ensembles were generated with Iwasaki $\times$ dislocation-suppressing-determinant-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV. The nucleon mass extrapolates to a value $m_N = 0.950(5)$ GeV at physical point. The isovector vector charge renormalizes to unity in the chiral limit, narrowly constraining excited-state contamination in the calculation. The ratio of the isovector axial-vector to vector charges shows a deficit of about ten percent. The tensor coupling no longer depends on mass and extrapolates to 1.04(5) in $\overline {\rm MS}$ 2-GeV renormalization at physical point, in a good agreement with the value obtained at the lightest mass in our previous calculations and other calculations that followed. The scalar charge, though noisier, does not show mass dependence and is in agreement with other calculations.

On the Correlation Energy of Interacting Fermionic Systems in the Mean-Field Regime

We consider a system of $$N\gg 1$$ interacting fermionic particles in three dimensions, confined in a periodic box of volume 1, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper and lower bounds for the correlation energy, which are optimal in their N-dependence. Moreover, we compute the correlation energy at leading order in the interaction potential, recovering the prediction of second order perturbation theory. The proof is based on the combination of methods recently introduced for the study of fermionic many-body quantum dynamics together with a rigorous version of second-order perturbation theory, developed in the context of non-relativistic QED.

Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality.

We study the prethermal dynamics of the Gross-Neveu-Yukawa quantum field theory, suddenly quenched in the vicinity of a critical point. We find that the universal prethermal dynamics is controlled by two fixed points depending on the size of the quench. Besides the usual equilibrium chiral Ising fixed point for a shallow quench, a dynamical chiral Ising fixed point is identified for a deep quench. Intriguingly, the latter is a nonthermal fixed point without any equilibrium counterpart due to the participation of gapless fermionic fields. We also find that in the scaling regime controlled by the equilibrium fixed point, the initial slip exponent is rendered negative if there are enough flavors of fermions, thus providing a unique signature of fermionic prethermal dynamics. We then explore the temporal crossover between the universal scaling regimes governed by the two universality classes. Possible experimental realizations are also discussed.

A classification of Markovian fermionic Gaussian master equations

We introduce a classification scheme for the generators of open fermionic Gaussian dynamics. We simultaneously partition the dynamics along the following four lines: (1) unitary versus non-unitary, (2) active versus passive, (3) state-dependent versus state-independent, and (4) single-mode versus multi-mode. We find that only nine of these 16 types of dynamics are possible. Using this partition we discuss the consequences of imposing complete positivity on fermionic Gaussian dynamics. In particular, we show that completely positive dynamics must be either unitary (and so can be implemented without an quantized environment) or active (and so must involve particle exchange with an environment).

Avoiding ergodicity problems in lattice discretizations of the Hubbard model

The Hubbard model arises naturally when electron-electron interactions are added to the tight-binding descriptions of many condensed matter systems. For instance, the two-dimensional Hubbard model on the honeycomb lattice is central to the ab initio description of the electronic structure of carbon nanomaterials, such as graphene. Such low-dimensional Hubbard models are advantageously studied with Markov chain Monte Carlo methods, such as Hybrid Monte Carlo (HMC). HMC is the standard algorithm of the lattice gauge theory community, as it is well suited to theories of dynamical fermions. As HMC performs continuous, global updates of the lattice degrees of freedom, it provides superior scaling with system size relative to local updating methods. A potential drawback of HMC is its susceptibility to ergodicity problems due to so-called exceptional configurations, for which the fermion operator cannot be inverted. Recently, ergodicity problems were found in some formulations of HMC simulations of the Hubbard model. Here, we address this issue directly and clarify under what conditions ergodicity is maintained or violated in HMC simulations of the Hubbard model. We study different lattice formulations of the fermion operator and provide explicit, representative calculations for small systems, often comparing to exact results. We show that a fermion operator can be found which is both computationally convenient and free of ergodicity problems.

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors: {a}_2^{pi }={0.101}_{-24}^{+24} for the pion; {a}_1^K={0.0533}_{-35}^{+34} and {a}_2^K={0.090}_{-20}^{+19} for the kaon. The calculation is carried out on 35 different CLS ensembles with Nf = 2 + 1 flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to a = 0.039 fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane.

Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation.

Quantum Brownian motion plays a fundamental role in many areas of modern physics. In the path-integral formulation, environmental fluctuations can be characterized by auxiliary stochastic fields. Intriguingly, for fermionic environments the stochastic fields must be Grassmann valued so as to memorize the order of the random forces exerted on the system. Such nonclassical fields cannot be represented by conventional means. We propose a strategy to map the Grassmann-number fields to conventional c-number noises and a set of quantized pseudolevels. The resulting stochastic equation of motion (SEOM) enables direct stochastic simulation of the fermionic dissipative dynamics. The SEOM gives exact physical observables of noninteracting systems, and yields accurate approximate results for interacting systems. The practicality and accuracy of the proposed strategy and the SEOM are exemplified by numerical studies conducted on a single-impurity Anderson model.

Quantum computation from fermionic anyons on a one-dimensional lattice

Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear optical model which allows for universal quantum computation.

Erratum: Critical behavior of reduced QED4,3 and dynamical fermion gap generation in graphene [Phys. Rev. D 94 , 114010 (2016)

Received 28 May 2019DOI:https://doi.org/10.1103/PhysRevD.99.119902© 2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDynamical symmetry breaking modelsLower-dimensional field theoriesMetal-insulator transitionNonperturbative effects in field theoryQuantum electrodynamicsSemimetalsPhysical SystemsGrapheneCondensed Matter, Materials & Applied PhysicsParticles & Fields

Chiral kinetic theory from effective field theory revisited

We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the O(1/μ) expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.

Pseudospin-dependent Zitterbewegung in monolayer graphene

We propose a spintronic device based on a narrow nanoribbon patterned from a monolayer graphene (MLG) sheet, embedded between a film of hexagonal boron nitride and a SiO2 substrate, all comprised under a three top-gated structure, to explore spin-dependent quantum transport of Dirac fermions. We developed a theoretical procedure for describing the pseudospin-related effects and the dynamics of Dirac fermions represented by a one-dimensional Gaussian wave packet (1DGWP), which is electrostatically confined in the device. The free-space 1DGWP time evolution follows expected features. Meanwhile, due to the weak breakdown of the real-spin degeneracy, the 1DGWP barely splits inside the under-barrier region governed by the extrinsic Rashba spin–orbit interaction (SOI-R). Most importantly, departing from the pristine MLG, we have found evidence of trembling antiphase oscillations in the probability density time-distribution for each sublattice state, which we have called the pseudospinorial Zitterbewegung effect (PZBE). The PZBE appears modulated with robust transient character and with a decay time in the femtosecond scale. Interestingly, several features of the PZBE become tunable, even its complete disappearance at the vicinity of the Dirac points or at a symmetric pseudospin configuration. For the proposed quasi-1D MLG device, we have captured evidence of the familiar Klein tunneling and the unusual anti-Klein tunneling, whose interplay for 2D MLG under tunable SOI-R was reported recently.

Partial compositeness and baryon matrix elements on the lattice

Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an SU(4) gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the scenario of obtaining a realistic top mass in this model.

Dirac Fermion and Plasmon Dynamics in Graphene and 3D Topological Insulators

AbstractLight–matter interactions illuminate the nature of solids and provide a second look on associated carrier dynamics. In particular, graphene and 3D topological insulators (3D TI) with broadband electromagnetic excitation have revealed to host exotic dynamic interactions. Much of Dirac‐point physics arises from discrete lattice symmetries and nontrivial Z2 classification of Bloch states. In this review, ongoing spectroscopic works on graphene and 3D TI are presented, where special attention is on the far‐infrared terahertz (THz) spectroscopy that characterizes the intraband dynamics. The constant absorbance of graphene upon interband particle–hole generation exhibits nonclassical results of gapless dispersion, which can be elucidated by the relativistic Dirac equations with zero rest mass. The massless Dirac fermions on graphene and 3D TI surface exhibit distinct phenomena compared to the conventional systems. First, the transient responses after pulse excitation reveal the semimetallic states of the gapless electronic dispersion, where the Fermi energy in equilibrium determines the crossover from metallic to semiconducting states. Second, the 2D Dirac plasmon dispersion of graphene and 3D TI surface exhibits unconventional density dependence in comparison to the massive electronic systems. The novel optical phenomena in graphene and 3D TI surface can serve for advanced optoelectronic and optospintronic applications.

Zooming in on fermions and quantum gravity

We zoom in on the microscopic dynamics for fermions and quantum gravity within the asymptotic-safety paradigm. A key finding of our study is the unavoidable presence of a nonminimal derivative coupling between the curvature and fermion fields in the ultraviolet. Its backreaction on the properties of the Reuter fixed point remains small for finite fermion numbers within a bounded range. This constitutes a nontrivial test of the asymptotic-safety scenario for gravity and fermionic matter, additionally supplemented by our studies of the momentum-dependent vertex flow which indicate the subleading nature of higher-derivative couplings. Moreover our study provides further indications that the critical surface of the Reuter fixed point has a low dimensionality even in the presence of matter.

Quantum simulation of the Weyl equation with a trapped ion

The Weyl equation describes chiral massless relativistic particles, called Weyl fermions, which have important relations to neutrinos. A direct observation of the dynamics of Weyl fermions in an experiment is difficult to achieve. This study investigates a method of simulating the Weyl equation in 1+2-dimension by a single trapped ion. The predictions about a two-dimensional Zitterbewegung and an especially interesting phenomenon of Weyl fermions can be tested by the future trapped ion experiment, which might enhance our understanding of neutrinos.

Sub-GeV-scale signatures of hidden braneworlds up to the Planck scale in a SO(3,1)-broken bulk

Many-brane Universes are at the heart of several cosmological scenarios related to physics beyond the Standard Model. It is then a major concern to constrain these approaches. Two-brane Universes involving [Formula: see text]-broken 5D bulks are among the cosmological models of interest. They also allow considering matter exchange between branes, a possible way to test these scenarios. Neutron disappearance (reappearance) toward (from) the hidden brane is currently tested with high-precision experiments to constrain the coupling constant [Formula: see text] between the visible and hidden neutron sectors. When dealing with the sub-GeV-scale quantum dynamics of fermions, any pair of braneworlds can be described by a noncommutative two-sheeted space–time [Formula: see text] from which [Formula: see text] emerges. Nevertheless, the calculation of the formal link between [Formula: see text] for a neutron and [Formula: see text]-broken 5D bulks remains an open problem until now although necessary to constrain these braneworld scenarios. Thanks to a phenomenological model, we derive [Formula: see text] — for a neutron — between the two braneworlds endowed with their own copy of the Standard Model in an [Formula: see text]-broken 5D bulk. Constraints on interbrane distance and brane energy scale (or brane thickness) are discussed. While brane energy scale below the GUT scale is excluded, energy scale up to the Planck limit allows neutron swapping detection in forthcoming experiments.

Observation of approximate SU(2)CS and SU(2nf) symmetries in high temperature lattice QCD

We study spatial isovector J = 1 meson correlators in nf = 2 QCD with dynamical domain-wall fermions on 323 × 8 lattices at temperatures T = 220–380 MeV. We observe an approximate degeneracy of all considered correlators with increasing temperature. This approximate degeneracy suggests emergent SU(2)CS and SU(2nf) symmetries at high temperatures, that mix left- and right-handed quarks. Since these symmetries are symmetries of the chromo-electric interaction in QCD we conclude that at 2Tc temperature the elementary objects are quarks with a definite chirality connected by the chromo-electric field.

Negative Temperature for Negative Lapse Function

Fermion dynamics distinguishes spacetimes having the same metric $g_{\mu\nu}$, but different tetrads $e_{\mu a}$, and in particular, it distinguishes a lapse with negative sign, $N<0$.[1] Here we show that the quasiequilibrium thermodynamic state may exist, in which the region with $N<0$ has negative local temperature $T({\bf r})<0$, while the global Tolman temperature $T_0$ remains positive. For bosons, only $N^2$ matters. However, if bosons are composite, they may inherit the negative $T({\bf r})$ from the fermions, and thus they may distinguish the spacetimes with positive and negative lapse functions via thermodynamics.