Limit Of Fermions Research Articles

Amplitude factorization in the electroweak standard model

We provide tools to analyze factorization at the amplitude level for processes involving the entire standard model. We focus in particular on a momentum region, in which the factorization of real and certain virtual corrections appears in a generalized eikonal approximation in which we expand around a quasisoft limit for massive gauge bosons, fermions, and scalars. We use the chirality-flow formalism to express loop exchanges or emissions as operators on chiral structures. This provides key tools for amplitude evolution with parton exchange and branching in the full Standard Model, including the electroweak sector. Published by the American Physical Society 2024

Universal constraints on energy flow and SYK thermalization

We study the dynamics of a quantum system in thermal equilibrium that is suddenly coupled to a bath at a different temperature, a situation inspired by a particular black hole evaporation protocol. We prove a universal positivity bound on the integrated rate of change of the system energy which holds perturbatively in the system-bath coupling. Applied to holographic systems, this bound implies a particular instance of the averaged null energy condition. We also study in detail the particular case of two coupled SYK models in the limit of many fermions using the Schwinger-Keldysh non-equilibrium formalism. We solve the resulting Kadanoff-Baym equations both numerically and analytically in various limits. In particular, by going to low temperature, this setup enables a detailed study of the evaporation of black holes in JT gravity.

Multiple Landau level filling for a large magnetic field limit of 2D fermions

Motivated by the quantum hall effect, we study N two dimensional interacting fermions in a large magnetic field limit. We work in a bounded domain, ensuring finite degeneracy of the Landau levels. In our regime, several levels are fully filled and inert: the density in these levels is constant. We derive a limiting mean-field and semi classical description of the physics in the last, partially filled Landau level.

Fermionic physics from abinitio path integral Monte Carlo simulations of fictitious identical particles.

The abinitio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion signproblem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the signproblem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the signproblem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

Looking at QED with Dyson–Schwinger Equations: Basic Equations, Ward–Takahashi Identities and the Two-Photon-Two-Fermion Irreducible Vertex

A minimal truncated set of the integral Dyson–Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations for the fermion and photon propagators, the photon-fermion vertex, and the two-photon-two-fermion one-particle-irreducible diagram. If the first three equations are exact, to build a closed set of equations, the two-photon-two-fermion equation is truncated ignoring the contribution of Green functions with large number of external legs. It is shown that the truncated equation for the two-photon-two-fermion vertex reproduces the lowest-order perturbative result in the limit of the small coupling constant. Furthermore, this equation allows to define an iterative procedure to compute higher order corrections in the coupling constant. The Ward–Takahashi identity for the two-photon-two-fermion irreducible vertex is derived and solved in the soft photon limit, where one of the photon momenta vanish, in the low photon momenta limit and for general kinematics. The solution of the Ward–Takahashi identity determines the longitudinal component of the two-photon-two-fermion irreducible vertex, while it is proposed to use the Dyson–Schwinger equation to determine the transverse part of this irreducible diagram. The two-photon-two-fermion DSE is solved in heavy fermion limit, considering a simplified version of the QED vertices. The contribution of this irreducible vertex to a low-energy effective photon-fermion vertex is discussed and the fermionic operators that are generated are computed in terms of the fermion propagator functions.

Fermi surface symmetric mass generation

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.

Fractionalization and Topology in Amorphous Electronic Solids.

Band topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wave functions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an amorphous setting. In this Letter, we extend these studies to incorporate the effect of strong repulsive interactions on the fate of topology and other correlation induced phenomena. Using a parton-based mean-field approach, we obtain the interacting phase diagram for an electronic two-orbital model with tunable topology in a two-dimensional amorphous network. In addition to the (non-)topological phases that are adiabatically connected to the free fermion limit, we find a number of strongly interacting amorphous analogs of crystalline Mott insulating phases with nontrivial chiral neutral edge modes, and a fractionalized Anderson insulating phase. The amorphous networks thus provide a new playground for studying a plethora of exotic states of matter, and their glassy dynamics, due to the combined effects of nontrivial topology, disorder, and strong interactions.

A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations ψ αL(R) → ψ αL(R) + n α z ψL(R) in the flavor space, where n α and z ψL(R) stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that n α can be identified as the elements U αi in the ith column of the unitary matrix U used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix M ψ , and m i = 0 holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

Impact of Chen-Ning Yang’s theoretical work on ultracold atomic physics

As early as the 1950s, Prof. Yang and his collaborators realized that the most important interaction effects in a dilute quantum gas can be described by the s-wave scattering length between particles. This insight leads to universal descriptions of the interaction effects without the detailed knowledge of the interaction potential. They derived a formula expanding the energy density in terms of the gas parameter. This formula is later known as the Lee-Huang-Yang correction. However, it took forty years for the experimentalists to overcome several challenges and finally achieve degenerate quantum gases of atoms in 1995. The developments after 1995 have led to an exciting field known as “quantum gases” or “ultracold atomic gases”. The ultracold atom system has flexible tunability, allowing both the scattering length and the dimensionality to vary. The Lee-Huang-Yang corrections were observed from several experiments on ultracold atoms by increasing the scattering length. In addition, by reducing the dimensionality to one-dimension, several experiments on ultracold atoms have confirmed the Yang-Yang thermodynamics for one-dimensional bosons that Prof. Yang obtained in the 1960s and the large-&lt;i&gt;N&lt;/i&gt; limit of one-dimensional fermions that Prof. Yang obtained around 2010. By increasing the dimensionality through using the idea of synthetic dimension, the experiment on ultracold atoms has also demonstrated the Yang monopole in the&lt;i&gt; SU&lt;/i&gt;(2) non-abelian gauge field proposed by Prof. Yang in the 1970s. All of these experiments show the long-lasting impact of Prof. Yang’s theoretical work over several decades.

Quantum Heat Engines with Singular Interactions

By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as anyons subject to Haldane’s generalized exclusion statistics. Solving the dynamics analytically using the framework of “statistical anyons”, we explore the interplay between interparticle interactions and wave function symmetry on engine performance.

Elementary example of exact effective-Hamiltonian computation

We present an exact computation of effective Hamiltonians for an elementary model obtained from the Yukawa theory by going to the limit of bare fermions being infinitely heavy and bare bosons being at rest with respect to the fermions that emit or absorb them. The coupling constant can be arbitrarily large. The Hamiltonians are computed by solving the differential equation of the renormalization group procedure for effective particles (RGPEP). Physical fermions, defined in the model as eigenstates of the effective Hamiltonians, are obtained in the form of an effective fermion dressed with a coherent state of effective bosons. The model computation illustrates the method that can be used in perturbative computations of effective Hamiltonians for realistic theories. It shows the mechanism by which the perturbative expansion and Tamm-Dancoff approximation increase in accuracy along the RGPEP evolution.

Calogero–Sutherland system at a free fermion point

We present two ways to obtain precise expressions for the commuting Hamiltonians of the integrable system regarded as a fermionic limit of the quantum Calogero–Sutherland system as the number of particles tends to infinity with some special values of the coupling constant $$\beta$$ . The construction is realized in the Fock space.

Soluble limit and criticality of fermions in Z2 gauge theories

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, we introduce a simple model for fermions moving in the deconfined phase of a $\mathbb Z_2$ gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code, permits us to tune the groundstate between an orthogonal metal and an orthogonal semimetal, in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a novel diagrammatic technique we are able to explore physics beyond the integrable point, to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit thus providing an important link between quantum materials and quantum information theory.

Convergence of nuclear effective field theory with perturbative pions

The classic paper by Fleming, Mehen and Stewart cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage and Wise to construct nuclear effective field theory around the unitary fermion limit with perturbative pion exchange. FMS identified the subclass of iterated one-pion exchange potential graphs as the cause of this poor convergence, which they showed persisted in the chiral limit. Theoretical tools are developed here to compute these Feynman graphs analytically to high order in all angular momentum channels simultaneously, examining the amplitudes computed to seven loops in the $L=J$ channels, and three loops in the coupled $L=J\pm1$ channels. One finds that there is nothing pathological about the perturbative expansion of a $1/r^3$ potential in general, and that the expansion converges satisfactorily in all partial waves except those with the lowest angular momentum, particularly the ${}^3P_0$ and the coupled ${}^3S_1-{}^3D_1$ channels. The results corroborate work by Birse, which suggests possible avenues to explore for improving the range of validity of the EFT expansion.

Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system

We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with N fermionic particles, where N tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit formulas for limits of Dunkl operators and the Yangian generators are presented by means of fermionic fields.

Quantum oscillation beyond the quantum limit in pseudospin Dirac materials

Recently, many unexpected fine structures in electric, magnetic, and thermoelectric responses at extremely magnetic fields in topological materials have attracted tremendous interest. We propose a new mechanism of quantum oscillation beyond the strong-field quantum limit for Dirac fermions. The amplitude of the oscillation is far larger than the usual Shubnikov--de Haas oscillation. The oscillation tends to be periodic in the magnetic field B, instead of 1/B. The period of the oscillation does not depend on the Fermi energy. These behaviors cannot be described by the famous Lifshitz-Kosevich formula. The oscillation arises from a mechanism that we refer to as the inversion of the lowest Landau level, resulted from the competition between the pseudospin Dirac-type Landau levels and real-spin Zeeman spitting beyond the quantum limit. This inversion gives rise to the oscillation of the Fermi energy and conductivity at extremely large magnetic fields. This mechanism will be useful for understanding the unexpected fine structures observed in the strong-field quantum limit in Dirac materials.

Parafermion theory from the q-deformed algebra with q a root of unity

In this paper, we find the [Formula: see text]-deformed algebra with the finite- and infinite-dimensional Fock space and both the fermionic limit and the bosonic limit. Using the cardinality of set theory, we propose the Hamiltonian interpolating bosonic case and fermionic case, which enables us to construct the proper partition function and internal energy. As examples, we discuss the specific heat of free [Formula: see text] parafermion gas model and [Formula: see text] parafermion star.

Quantum entanglement in one-dimensional anyons

Anyons in one spatial dimension can be defined by correctly identifying the configuration space of indistinguishable particles and imposing Robin boundary conditions. This allows an interpolation between the bosonic and fermionic limits. In this paper, we study the quantum entanglement between two one-dimensional anyons on a real line as a function of their statistics.

The HTL Lagrangian at NLO: The photon case

We calculate the two loop hard correction to the photon self-energy in an electron-positron plasma (EPP) for arbitrary soft momenta. This provides the only missing ingredient to obtain the Hard Thermal Loop (HTL) effective Lagrangian at next-to-leading order (NLO), and the full photon propagator at the same order. This result can be easily extended to obtain the soft photon propagator in a quark gluon plasma. We use the Keldysh representation of the real time formalism in the massless fermion limit, and dimensional regularization (DR) to regulate any ultraviolet (UV), infrared (IR) or collinear divergences that appear in the intermediate steps of the calculation. In the limit of soft photon momenta, our result is finite. It not only provides an O(α) correction to the Debye mass, but also a new non-local structure. A consistent regularization of radial and angular integrals is crucial to get this new structure. As an application we calculate the plasmon dispersion relations at NLO.

Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling

In 2+1 dimensions, QED becomes exactly solvable for all values of the fermion charge $e$ in the limit of many fermions $N_f\gg 1$. We present results for the free energy density at finite temperature $T$ to next-to-leading-order in large $N_f$. In the naive large $N_f$ limit, we uncover an apparently UV-divergent contribution to the vacuum energy at order ${\cal O}(e^6 N_f^3)$, which we argue to become a finite contribution of order ${\cal O}(N_f^4 e^6)$ when resumming formally higher-order $1/N_f$ contributions. We find the finite-temperature free energy to be well-behaved for all values of the dimensionless coupling $e^2N_f/T$, and to be bounded by the free energy of $N_f$ free fermions and non-interacting QED3, respectively. We invite follow-up studies from finite-temperature lattice gauge theory at large but fixed $N_f$ to test our results in the regime $e^2N_f/T\gg 1$.