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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Magnetic photocurrents in multifold Weyl fermions

Here, we examine the magneto-optical response of chiral multifold fermions. Specifically, we show that they are ideal candidates for observing the helical magnetic effect (HME) previously predicted for simple Weyl fermions. Unlike Weyl fermions, the HME is present in multifold fermions even in the simplest case where the low-energy dispersion is linear and spherically symmetric. In this ideal case, we derive an analytical expression for the HME and find it is proportional to the circular photogalvanic effect; for realistic parameters and accounting for the geometry of the setup, the HME photocurrent could be roughly the same order of magnitude as the circular photogalvanic effect observed in multifold fermions. Additional nonlinear and symmetry-breaking terms will ruin the quantization but not hurt the observation of the HME.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Coupling of magnetism and Dirac fermions in YbMnSb 2

Here, we report inelastic neutron scattering measurements of magnetic excitations in YbMnSb 2 , a low-carrier-density Dirac semimetal in which the antiferromagnetic Mn layers are interleaved with Sb layers that host Dirac fermions. We observe a measurable broadening of spin waves, which is consistent with substantial spin-fermion coupling. The spin-wave damping γ in YbMnSb 2 is roughly twice larger compared to that in a sister material, YbMnBi 2 , where an indication of a small damping consistent with a theoretical analysis of the spin-fermion coupling was reported. The interplane interaction between the Mn layers in YbMnSb 2 is also much stronger, suggesting that the interaction mechanism is rooted in the same spin-fermion coupling. Our results establish the systematics of spin-fermion interactions in layered magnetic Dirac materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Four-fermion deformations of the massless Schwinger model and confinement

We consider the massless charge-N Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, and respects a Z 2 subgroup of chiral symmetry for even N, hence forbidding a mass term. When it is relevant, even the exactly massless theory exhibits both confinement and spontaneous chiral symmetry breaking. The construction is analogous to QCD(adj) in 2d. While the theory without four-fermion deformations is deconfined, the theory with these deformations is generically in a confining phase. We study the model on R 2 using bosonization, and also analyze the mechanism of confinement on R × S 1 , where we find that confinement is driven by fractional instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Evidence for Topological Protection Derived from Six-Flux Composite Fermions

The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor ν = 9/11, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Two-dimensional heavy fermions in the van der Waals metal CeSiI

Heavy-fermion metals are prototype systems for observing emergent quantum phases driven by electronic interactions. A long-standing aspiration is the dimensional reduction of these materials to exert control over their quantum phases, which remains a significant challenge because traditional intermetallic heavy-fermion compounds have three-dimensional atomic and electronic structures. Here we report comprehensive thermodynamic and spectroscopic evidence of an antiferromagnetically ordered heavy-fermion ground state in CeSiI, an intermetallic comprising two-dimensional (2D) metallic sheets held together by weak interlayer van der Waals (vdW) interactions. Owing to its vdW nature, CeSiI has a quasi-2D electronic structure, and we can control its physical dimension through exfoliation. The emergence of coherent hybridization of f and conduction electrons at low temperature is supported by the temperature evolution of angle-resolved photoemission and scanning tunnelling spectra near the Fermi level and by heat capacity measurements. Electrical transport measurements on few-layer fakes reveal heavy-fermion behaviour and magnetic order down to the ultra-thin regime. Importantly, our work establishes CeSiI and related materials as a unique platform for studying dimensionally confined heavy fermions in bulk crystals and employing 2D device fabrication techniques and vdW heterostructures to manipulate the interplay between Kondo screening, magnetic order and proximity effects.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems

The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Here, our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicate that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams, and provides a better starting point for addressing challenging spin problems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Hartree–Fock–Bogoliubov theory for number-parity-violating fermionic Hamiltonians

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan–Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree–Fock–Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. Here, we also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Fermionic mean-field theory as a tool for studying spin Hamiltonians

The Jordan–Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Furthermore, Jordan–Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J 1 –J 2 Heisenberg models, as well as to the pairing or reduced Bardeen–Cooper–Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Chiral Dirac Fermion in a Collinear Antiferromagnet

In a Dirac semimetal, the massless Dirac fermion has zero chirality, leading to surface states connected adiabatically to a topologically trivial surface state as well as vanishing anomalous Hall effect. Recently, it is predicted that in the nonrelativistic limit of certain collinear antiferromagnets, there exists a type of chiral "Dirac-like" fermion, whose dispersion manifests four-fold degenerate crossing points formed by spin-degenerate linear bands, with topologically protected Fermi arcs. Such an unconventional chiral fermion, protected by a hidden SU(2) symmetry in the hierarchy of an enhanced crystallographic group, namely spin space group, is not experimentally verified yet. Here, by angle-resolved photoemission spectroscopy measurements, we reveal the surface origin of the electron pocket at the Fermi surface in collinear antiferromagnet CoNb 3 S 6 . Combining with neutron diffraction and first-principles calculations, we suggest a multidomain collinear antiferromagnetic configuration, rendering the the existence of the Fermi-arc surface states induced by chiral Dirac-like fermions. Finally, our work provides spectral evidence of the chiral Dirac-like fermion caused by particular spin symmetry in CoNb 3 S 6 , paving an avenue for exploring new emergent phenomena in antiferromagnets with unconventional quasiparticle excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Non-perturbative production of fermionic dark matter from fast preheating

We investigate non-perturbative production of fermionic dark matter in the early universe. We study analytically the gravitational production mechanism accompanied by the coupling of fermions to the background inflaton field. The latter leads to the variation of effective fermion mass during preheating and makes the resulting spectrum and abundance sensitive to its parameters. Assuming fast preheating that completes in less than the inflationary Hubble time and no oscillations of the inflaton field after inflation, we find an abundant production of particles with energies ranging from the inflationary Hubble rate to the inverse duration of preheating. The produced fermions can account for all observed dark matter in a broad range of parameters. As an application of our analysis, we study non-perturbative production of fermionic dark matter in the model of Palatini Higgs inflation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Infrared fixed points of higher-spin fermions in topological semimetals

We determine the fate of interacting fermions described by the Hamiltonian H = p ∙ J in three-dimensional topological semimetals with linear band crossing, where p is momentum and J are the spin- j matrices for half-integer pseudospin j ≥ 3/2. While weak short-range interactions are irrelevant at the crossing point due to the vanishing density of states, weak long-range Coulomb interactions lead to a renormalization of the band structure. Using a self-consistent perturbative renormalization group approach, we show that band crossings of the type p ∙ J are unstable for j ≤ 7/2. Instead, through an intriguing interplay between cubic crystal symmetry, band topology, and interaction effects, the system is attracted to a variety of infrared fixed points. We also unravel several other properties of higher-spin fermions for general j , such as the relation between fermion self-energy and free energy, or the vanishing of the renormalized charge. An O(3) symmetric fixed point composed of equal chirality Weyl fermions is stable for j ≤ 7/2 and very likely so for all j. We then explore the rich fixed point structure for j = 5/2 in detail. We find additional attractive fixed points with enhanced O ( 3 ) symmetry that host both emergent Weyl or massless Dirac fermions, and identify a puzzling, infrared stable, anisotropic fixed point without enhanced symmetry in close analogy to the known case of j = 3/2.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Soluble limit and criticality of fermions in $\mathbb Z_2$ 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, in this paper 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 ground state 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 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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Enhancement of charge-neutral fermionic excitations near the spin-flop transition in the magnetic Kondo material YbIr 3 Si 7

The new Kondo material YbIr 3 Si 7 , similar to other Kondo insulators, has been reported to exhibit charge-neutral fermionic excitations through measurements of specific heat and thermal conductivity at low temperatures. We performed 29 Si-NMR on YbIr 3 Si 7 to investigate the magnetic response of charge-neutral fermions from a microscopic perspective. In low magnetic fields parallel to the c axis, a single NMR peak in the paramagnetic state splits into three peaks below TN. In contrast, only a slight shift of the single NMR peak was observed in high magnetic fields. This spectral change as a function of the c-axis magnetic field is interpreted as a spin-flop transition, at which the magnetic moments oriented along the c axis antiferromagnetic (AFM-I) phase are rotated to the ab plane with a ferromagnetic component along the c-axis (AFM-II phase). In the vicinity of the spin-flop magnetic field H M , the nuclear spin-lattice relaxation rate 1/T 1 was found to be proportional to temperature at low temperatures, indicating the existence of charge-neutral fermions. Furthermore, a peak of 1/T 1 versus the c-axis magnetic field suggests that the charge-neutral fermions in YbIr 3 Si 7 are closely related to its magnetic properties. Our findings shed light on the origin of charge-neutral fermions in insulators.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Two-fermion negativity and confinement in the Schwinger model

We consider the fermionic (logarithmic) negativity between two fermionic modes in the Schwinger model. Recent results pointed out that fermionic systems can exhibit stronger entanglement than bosonic systems, exhibiting a negativity that decays only algebraically. The Schwinger model is described by fermionic excitations at short distances, while its asymptotic spectrum is the one of a bosonic theory. We show that the two-mode negativity detects this confining, fermion-to-boson transition, shifting from an algebraic decay to an exponential decay at distances of the order of the de Broglie wavelength of the first excited state. We derive analytical expressions in the massless Schwinger model and confront them with tensor network simulations. We also perform tensor network simulations in the massive model, which is not solvable analytically, and close to the Ising quantum critical point of the Schwinger model, where we show that the negativity behaves as its bosonic counterpart. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Gauging staggered fermion shift symmetries

Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an S U ( 4 ) flavor symmetry which plays a crucial role in showing that staggered fermions lead to a theory of four degenerate Dirac fermions in the continuum limit. They are associated with the appearance of certain Z 2 valued global parameters. We propose a strategy to try to partially gauge these translation symmetries by allowing these parameters to vary locally in the lattice. To maintain invariance of the action requires the addition of Z 2 valued higher form lattice gauge fields. An analogous procedure can be carried out for reduced staggered fermions where the shifts correspond to a discrete subgroup of an S O ( 4 ) flavor symmetry. Published by the American Physical Society 2024

Catterall, Simon (ORCID:0000000327352682)↗
DOE OSTI2026

Neuralized fermionic tensor networks for quantum many-body systems

In this work, we describe a class of neuralized fermionic tensor network states (NN-fTNSs) that introduce nonlinearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNSs achieve order of magnitude improvements in the ground-state energy compared to pure fTNSs with the same bond dimension and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states based on Slater determinants and Pfaffians, NN-fTNSs offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNSs naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

A beginner's guide to non-abelian iPEPS for correlated fermions

Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension D=24 D = 24 on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with 2 2 bands of spinful fermions of \mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb} S U ( 2 ) s p i n ⊗ S U ( 2 ) o r b symmetry, the other with 3 3 flavors of spinless fermions of \mathrm{SU}(3)_\mathrm{flavor} S U ( 3 ) f l a v o r symmetry.

Bruognolo, Benedikt↗
DOE OSTI2022

Topological Crystalline Insulator Candidate ErAsS with Hourglass Fermion and Magnetic-Tuned Topological Phase Transition

Topological crystalline insulators (TCIs) with hourglass fermion surface state have attracted a lot of attention and are further enriched by crystalline symmetries and magnetic order. Here, the emergence of hourglass fermion surface state and exotic phases in the newly discovered, air-stable ErAsS single crystals are shown. In the paramagnetic phase, ErAsS is expected to be a TCI with hourglass fermion surface state protected by the nonsymmorphic symmetry. Dirac-cone-like bands and nearly linear dispersions in large energy range are experimentally observed, consistent well with theoretical calculations. Below T N ≈ 3.27 K, ErAsS enters a collinear antiferromagnetic state, which is a trivial insulator breaking the time-reversal symmetry. An intermediate incommensurate magnetic state appears in a narrow temperature range (3.27–3.65 K), exhibiting an abrupt change in magnetic coupling. Overall, the results reveal that ErAsS is an experimentally available TCI candidate and provide a unique platform to understand the formation of hourglass fermion surface state and explore magnetic-tuned topological phase transitions.

36 MATERIALS SCIENCE↗