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At least 37 records · Page 2
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DOE OSTI2024

Tensor renormalization group for fermions

Abstract We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson–Majorana fermions and multi-flavor Gross–Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Physics↗
DOE OSTI2025

Alternating and Gaussian Fermionic Isometric Tensor Network States

Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric tensor network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward; hence the name alternating isometric tensor network states. Second, we introduce a numerical tool—the isometric Gaussian fermionic TNS (isoGfTNS)—that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNSs represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNSs. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNSs mediate entanglement more efficiently than conventional isoTNSs. Second, alternating isoTNSs correspond to a deeper, and thus more representative, sequential-circuit construction of depth 𝒪⁢(𝐿𝑥 ⋅𝐿𝑦) compared to the original isoTNSs of depth 𝒪⁢(𝐿𝑥 +𝐿𝑦). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidence of better bond-dimension scaling and variational energy of alternating isoGfTNSs for ground states of various free-fermionic models, including the Fermi surface, the band insulator, and the 𝑝𝑥 +𝑖⁢𝑝𝑦 mean-field superconductor. Finally, benchmarking on the transverse-field Ising model, we demonstrate that an alternating isoTNS provides substantially improved performance and stability relative to the original isoTNS for the ground-state search algorithm in interacting systems.

Wu, Yantao [Chinese Academy of Sciences, Beijing (↗
DOE OSTI2026

Real-time simulation of asymmetry generation in fermion-bubble collisions

Motivated by the out-of-equilibrium dynamics during an early-Universe first-order phase transition, we perform real-time simulations of fermion-bubble scattering in 1 + 1 dimensions. This nonequilibrium process can generate a charge-conjugation C asymmetry outside the bubble wall, induced by the complex fermion mass profile. The resulting C asymmetry is the 1 + 1 -dimensional analog of the C P asymmetry in 3 + 1 dimensions, a key ingredient in baryon asymmetry generation at the electroweak scale. Using tensor network methods, we track the real-time evolution of the C asymmetry in the charge density as the fermion interacts with the bubble wall, a regime inaccessible to analytic calculations. We further introduce two observables to quantify the asymmetry in the asymptotic region where reflected particles are well separated from the scattering point: one based on the net charge outside the bubble wall, and the other on the spatial displacement between the reflected particle and antiparticle wave packets. Our study represents a first step toward nonperturbative, real-time computations of C P asymmetry in 3 + 1 dimensions for electroweak baryogenesis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Generative deep-learning reveals collective variables of Fermionic systems

Complex processes of fermionic systems ranging from protein folding to nuclear fission often follow a low-dimensional reaction path parametrized in terms of a few collective variables. In nuclear theory, variables related to the shape of the nuclear density in a mean-field picture are key to describing the large amplitude collective motion of the neutrons and protons. Exploring the adiabatic energy landscape spanned by these degrees of freedom reveals the possible reaction channels while simulating the dynamics in this reduced space yields their respective probabilities. Unfortunately, this theoretical framework breaks down whenever the systems encounters a quantum phase transition with respect to the collective variables. Here, in this study, we introduce a novel generative deep-learning algorithm designed to build reaction paths that ensure that the many-fermion wave function stays differentiable with respect to the collective variables. This approach is applicable to any fermionic system described by a coherent state. We use the case of potential energy curves in the 16 O nucleus within the Hartree-Fock theory to illustrate its main features.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system

We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation. Our numerical simulations using nHYP-smeared staggered fermions with Pauli-Villars improvement do not exhibit any first-order bulk phase transition in the investigated parameter region. We utilize an infinite volume renormalization scheme based on the gradient flow transformation to determine the renormalization group β function. The gradient flow β function exhibits a zero at g GF ⋆ 2 = 6.60 ( 62 ) , implying that the system is infrared conformal. We calculate the leading irrelevant critical exponent γ g ⋆ = 0.199 ( 32 ) . Our prediction for γ g ⋆ is consistent with available literature at the 1 − 2 σ level. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Causal fermion states in magnetic field in a relativistic rotating frame and electromagnetic radiation by a rapidly rotating charge

We consider the Dirac field uniformly rotating with angular velocity Ω and also subject to the constant magnetic field B directed along the rotation axis. The causal states are constrained to the interior of the light cylinder of radius c / Ω . When this radius is smaller than the system size, as in the quark-gluon plasma, the effect of the boundary on the fermion spectrum is critical. We derive the fermion spectrum and study its properties. We compute the intensity of the electromagnetic radiation emitted due to transitions between the fermion states. We study its dependence on energy and angular momentum for different values of the angular velocity and the magnetic field. Rotation has enormous impact on the electromagnetic radiation by the quark-gluon plasma with or without the magnetic field. Published by the American Physical Society 2024

Buzzegoli, Matteo (ORCID:0000000221145431)↗
DOE OSTI2025

Fermionic Isometric Tensor Network States in Two Dimensions

We generalize isometric tensor network states to fermionic systems, paving the way for efficient adaptations of 1D tensor network algorithms to 2D fermionic systems. As the first application of this formalism, we developed and benchmarked a time-evolving block-decimation (TEBD) algorithm for real-time and imaginary-time evolution. The imaginary-time evolution produces ground-state energies for gapped systems, systems with a Dirac point, and systems with gapless edge modes to good accuracy. Here, the real-time TEBD captures the scattering of two fermions and the chiral edge dynamics on the boundary of a Chern insulator.

2-dimensional systems↗
DOE OSTI2025

Monopole-Fermion Scattering and the Solution to the Semiton–Unitarity Puzzle

We study Polchinski’s “fermion-rotor system” as an accurate description of charged Weyl fermions scattering on a magnetic monopole core in the limit of zero gauge coupling. Traditionally it was thought such scattering could lead to fractional particle numbers (“semitons”). By direct calculations we show those semitonic processes are in fact free propagation, facilitated by composite fermion-rotor operators interpolating the “forbidden” states, effectively “recovering” both ingoing and outgoing states in every lowest partial wave. Nonsemitonic Callan-Rubakov processes are unchanged.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Evidence of Chiral Fermion Edge Modes through Geometric Engineering of Thermal Hall Effect in 𝛼−RuCl 3

The experimental observation of half-integer-quantized thermal Hall conductivity in the Kitaev candidate material α-RuCl 3 has served as a signature of non-Abelian anyons through an associated chiral Majorana edge mode. However, both the reproducibility of the quantized thermal Hall conductivity and the fundamental nature of the associated heat carriers, whether bosonic or fermionic, are subjects of ongoing and vigorous debate. In a recent theoretical work, it was proposed that varying the sample geometry through creating constrictions can distinguish between different origins of the thermal Hall effect in magnetic insulators. Here, in this study, we provide experimental evidence of chiral fermion edge modes by comparing the thermal Hall effect of a geometrically constricted α-RuCl 3 sample with that of an unconstricted sample. In contrast to the unconstricted crystals where the thermal Hall signal fades below 5 K, the constricted crystals display a significant thermal Hall signal that remains measurable even at 2 K. This sharp difference agrees well with the theoretical prediction and provides compelling evidence for the contribution of chiral fermion edge modes to the thermal Hall effect in α-RuCl 3 . More broadly, this work confirms that the geometry dependence of the thermal Hall effect can help identify chiral spin liquids in candidate materials like α-RuCl 3 and paves the way for the experimental realization of thermal anyon interferometry.

Zhang, Heda [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2024

Chiral symmetry and Atiyah-Patodi-Singer index theorem for staggered fermions

We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral symmetry of a continuum formulation of staggered fermions called Kähler-Dirac fermions, which have been recently investigated as an ingredient in lattice constructions of chiral gauge theories. We point out that there are two notions of chiral symmetry for Kähler-Dirac fermions, both having a mixed perturbative anomaly with gravity leading to index theorems on closed manifolds. By formulating these theories on a manifold with boundary, we find the APS index theorems corresponding to each of these symmetries, necessary for a complete picture of anomaly inflow, using a recently discovered physics-motivated proof. We comment on a fundamental difference between the nature of these two symmetries by showing that a sensible local, symmetric boundary condition only exists for one of the two symmetries. This sheds light on how these symmetries behave under lattice discretization, and in particular on their use for recent symmetric-mass generation proposals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Fingerprints of composite fermion Lambda levels in scanning tunneling microscopy

A composite fermion (CF) is a topological quasiparticle that emerges from a nonperturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to noninteracting fermions that form Landau levels in a magnetic field, CFs can fill analogous “Lambda” levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes the low-energy properties of CFs, we show that high-energy features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the noninteracting CF paradigm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Symmetries and anomalies of Hamiltonian staggered fermions

We review the shift (translation) and time reversal symmetries of Hamiltonian staggered fermions and their connection to continuum symmetries concentrating in particular on the case of massless fermions and (3+1) dimensions. We construct operators using the staggered fields that implement these symmetries on finite lattices. We show that shifts composed of an odd multiple of the elementary shift anticommute with time reversal and are related to continuum axial transformations. We argue that the presence of these nontrivial commutation relations implies the existence of lattice ’t Hooft anomalies. From the shifts we also construct a set of conserved, quantized charges that generate continuous symmetries of the lattice theory. In general these do not commute with the vector charge signaling further ’t Hooft anomalies.

Anomalies↗
DOE OSTI2025

Low-energy electrodynamics and a hidden Fermi liquid in the heavy-fermion compound CeCoIn 5

We present time-domain THz spectroscopy of thin films of the heavy-fermion superconductor CeCoIn 5 . Below the ≈40 K Kondo coherence temperature, a narrow Drude-like peak forms, as a result of the 𝑓-orbital–conduction-electron hybridization and the formation of the heavy-fermion state. The complex optical conductivity is analyzed through a Drude model and extended Drude model analysis. Via the extended Drude model analysis, we measure the frequency-dependent scattering rate (1/𝜏) and effective mass (𝑚*/𝑚 𝑏 ). This scattering rate shows a linear dependence on temperature, which matches the dependence of the resistivity as expected. Nevertheless, the width of the low-frequency Drude peak itself that is set by the renormalized quasiparticle scattering rate (1/𝜏*=𝑚 𝑏 /𝑚*⁢𝜏) shows a 𝑇 2 dependence. This is the scattering rate that characterizes the relaxation time of the renormalized quasiparticles. In conclusion, this gives evidence for a Fermi liquid state, which in conventional transport experiments is hidden by the strong temperature dependent mass.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Tensor network representation of non-abelian gauge theory coupled to reduced staggered fermions

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because reduced staggered fermions can be represented in terms of a minimal number of tensor indices while the gauge sector can be approximated using Gaussian quadrature with a truncation. Numerical results obtained using the Grassmann TRG algorithm are shown for the case of SU(2) lattice gauge theory and compared to Monte Carlo results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to $\overline{MS}$ with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ϵ [0.25, 0.75] at the largest pion momentum P z ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

A new-old approach to composite scalars with chiral fermion constituents

We develop a dynamical, Lorentz invariant theory of composite scalars in configuration space consisting of chiral fermions, interacting by the perturbative exchange of a massive “gluon” of coupling g 0 and mass M 0 2 (the coloron model). The formalism is inspired by, but goes beyond, old ideas of Yukawa and the Nambu-Jona-Lasinio (NJL) model. It yields a non-pointlike internal wave-function of the bound state, ϕ ( r ) , which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue μ 2 . For super-critical coupling, g 0 2 > g 0 c 2 , we have μ 2 < 0 leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, not loop-level as in NJL. The mass scale is determined by the interaction as in NJL. We mainly focus on the short-distance, large M 0 2 limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, ϕ ( r → ) , remains spatially extended and dilutes ϕ ( 0 ) . This leads to power-law suppression of the induced Yukawa and quartic couplings and requires radically less fine-tuning of a hierarchy than does the NJL model. We include a discussion of loop corrections of the theory. A realistic top condensation model appears possible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Emergence of Moiré Dirac Fermions at the Interface of Topological and 2D Magnetic Insulators

Dirac Fermions on the surface of the topological insulator are spin-momentum locked and topologically protected, making them interesting for spintronics and quantum computing applications. When in proximity to magnetism and superconductivity, these electronic states could result in quantum anomalous Hall effect and Majorana Fermions, respectively. An even more dramatic enrichment of the topological insulators’ physics is expected for moiré superlattices, where, analogously to the twisted graphene layers, electronic correlations could be strongly enhanced, a task previously notoriously difficult to achieve in topological matter. Until now, the experimental confirmation of such moiré properties has remained elusive. Here, we grow the two-dimensional van der Waals magnetic insulators FeX 2 (where X = Cl or Br) on top of the topological insulator Bi 2 Se 3 and establish a moiré superlattice formation at the interface. By means of scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we investigate the electronic properties of the formed moiré superlattice and demonstrate its tunability via the film choice. We reveal replicated Dirac cones and focus on their intersections, which, in the case of FeBr 2 /Bi 2 Se 3 , occur below the Fermi level. We identify the signatures of small gaps at the intersections around the M̅ i points that we attribute to the moiré interaction. These findings point to the specific type of magnetic moiré potential that breaks the time-reversal symmetry at these points but not at the $\barΓ$ point. Our observations provide an intriguing scenario of correlated topological phases induced by moiré superlattice that may result in topological superconductivity, high Chern number phases, and exotic noncollinear magnetic textures.

2D magnets↗
DOE OSTI2026

Realization of fermionic Laughlin state on a quantum processor

Strongly correlated topological phases of matter are central to modern condensed matter physics and quantum information technology but often challenging to probe and control in material systems. The experimental difficulty of accessing these phases has motivated the use of engineered quantum platforms for simulation and manipulation of exotic topological states. Among these, the Laughlin state stands as a cornerstone for topological matter, embodying fractionalization, anyonic excitations, and incompressibility. Although its bosonic analogs have been realized on programmable quantum simulators, a genuine fermionic Laughlin state has yet to be demonstrated on a quantum processor. Here, we realize the ν = 1/3 fermionic Laughlin state on IonQ’s trapped-ion quantum computer using an efficient and scalable Hamiltonian variational ansatz with 369 two-qubit gates on a 16-qubit circuit. Employing symmetry-verification error mitigation, we extract key observables that characterize the Laughlin state, including correlation hole, bulk-edge correspondence, and topological entanglement entropy, with strong agreement to exact diagonalization benchmarks. This work demonstrates an end-to-end workflow to simulate material-intrinsic topological orders and provides a starting point to explore its dynamics and excitations on digital quantum processors.

Shen, Lingnan [Univ. of Washington, Seattle, WA (U↗