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For this work, we apply a variational ansatz based on neural networks to the problem of spin-$^1_2$ fermions in a harmonic trap interacting through a short distance potential. We showed that standard machine learning techniques lead to a quick convergence to the ground state, especially in weakly coupled cases. Higher couplings can be handled efficiently by increasing the strength of interactions during “training”.
Evidence for developing fractional quantum Hall effect (FQHE) at filling fraction 𝜈 = 1/6 and 1/8 was recently reported in wide GaAs quantum wells [Wang et al., Phys. Rev. Lett. 134, 046502 (2025)]. In this article, we theoretically investigate the nature of the state at 𝜈 = 1/6 as a function of the quantum well width and the density by considering composite-fermion (CF) crystals, CF Fermi sea, and various kinds of paired CF states. The 𝑓-wave paired state has the lowest energy among the paired CF states. However, for parameters of interest, the energies of the CF crystal, the CF Fermi liquid, and the 𝑓-wave paired CF state are too close to distinguish. We, therefore, predict that 𝑖𝑓 the FQHE at 𝜈 = 1/6 is experimentally confirmed, this state would be an 𝑓-wave paired state of CFs, which can be verified by measurement of its thermal Hall conductance. Exact diagonalization studies on clean systems with up to eight electrons show that the ground states at 𝜈 = 𝑛/(6𝑛 ± 1) are incompressible for all widths and densities we have considered, and are well described by the corresponding Laughlin and Jain states. We propose a phase diagram for large quantum well widths and densities in which at zero disorder, incompressible FQHE states are stabilized at 𝜈 = 𝑛/(6𝑛 ± 1) and 𝜈 = 1/6, but in between these fillings the CF crystal is stabilized. We also present a qualitative discussion on the effects of disorder and propose a schematic phase diagram based on it. With disorder, which creates a spatial variation in the filling factor, two regimes are identified: (i) for small disorder, when the incompressible states percolate at the special fillings, FQHE with quantized Hall plateaus and vanishing longitudinal resistance should occur; and (ii) for larger disorder, when the CF crystal percolates, the longitudinal resistance rises with decreasing temperature but the domains of FQHE liquid produce minima at the special filling factors. Here, experiments are consistent with the latter scenario. We also mention a possible connection of the phase diagram presented here to a puzzling behavior observed for the fractional quantum anomalous Hall effect in pentalayer graphene.
We report on our study of the electron interaction effects in topological two-dimensional (2D) materials placed in a quantizing magnetic field. Taking our cue from a recent experimental report, we consider a particular case of bismuthene monolayer with a strong spin-orbit interaction which can be a Weyl semimetal when placed on a specially tuned substrate. Interestingly, we observe that in some Landau levels of this material, the interaction effects are enhanced compared to those for a conventional 2D system and graphene monolayer. Such an enhancement of electron-electron interactions in these materials is largely due to an anisotropy present in the materials. Additionally, the interaction effects can be tuned by changing the coupling to the substrate and the strongest inter-electron interactions are observed when the system is a Weyl semimetal. Furthermore, the observed enhancement of the interaction effects can therefore be an important signature of the 2D Weyl fermions.
Coherent paired states for strongly interacting fermions
First-order density matrix corresponding to nondegenerate eigenstate be N-representable for time-reversal invariant Hamiltonian and quantum- mechanical system of N identical fermions
We study the symmetries of lattice staggered fermions in 2+1d. Using the symmetries, we can place the system on any sheared torus or Klein bottle. These different backgrounds provide diagnostics of various ’t Hooft anomalies associated with the crystalline symmetries. We then compare the lattice model to its continuum limit. The symmetries of the lattice system are mapped in a nontrivial way to the symmetries of the continuum theories. Using this map, we match the ’t Hooft anomalies on the lattice and the continuum. Along the way, we develop a general formalism to study Hamiltonian lattice models on nontrivial, compact, flat spaces.
A modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD is presented. A larger basis of test vectors than that used in regular multigrid is calculated by the smoother and truncated by singular value decomposition on the chiral components of the test vectors. The truncated basis is used to form the prolongation and restriction matrices of the multigrid hierarchy. This modification of the setup method is demonstrated to increase the convergence of linear solvers on an anisotropic lattice with m π ≈ 239 MeV from the Hadron Spectrum Collaboration and an isotropic lattice with m π ≈ 220 MeV from the MILC Collaboration. The lattice volume dependence of the method is also examined. Increasing the number of test vectors improves speedup up to a point, but storing these vectors becomes impossible in limited memory resources such as GPUs. To address storage cost, we implement a streaming singular value decomposition of the basis of test vectors on the chiral components and demonstrate a decrease in the number of fine level iterations by a factor of 1.7 for m q ≈ m crit
Polycrystalline Mn 5 SiC was synthesized by using a high-temperature solid-state method. Mn 5 SiC adopts a polar space group (Cmc2 1 ) with six crystallographic Mn sites confirmed by X-ray and neutron diffraction, transmission electron microscopy, and second harmonic generation experiments. The complex crystal structure features edge-sharing trigonal prisms and icosahedra, as well as face/edge-sharing pentagonal prisms. Magnetic measurements indicate ferrimagnetic ordering with a transition temperature of 284 K. The ferrimagnetic structure (magnetic space group Cm’c’2 1 ) was further identified by powder neutron diffraction, where collinear Mn spins align along the crystallographic c-axis. The refined magnetic moment for each crystallographic Mn site at 4 K is 1.8(2), −2.42(9), −1.72(8), 0.51(6), 0.50(4), and 1.7(2) μ B . Density functional theory calculations confirm both the metallic behavior and the ferrimagnetic structure observed experimentally and further provide insight into the observed Mn moment dependence across crystallographic sites. The resistivity and specific heat measurements and density functional theory calculations reveal a substantially large Kadowaki–Woods ratio of 5 × 10 –5 μΩ·cm/(mJ/mol) 2 and a many-body renormalization factor of 5.5, indicating the unusual heavy Fermion behavior in such an itinerant magnetic metal.
Seniority is a useful way of organizing Hilbert space for strongly correlated systems. The exact zero-seniority wave function, doubly occupied configuration interaction (DOCI), provides accurate results (given the right orbitals) for many strongly correlated electronic systems but has a combinatorial computational cost. In many cases, pair coupled cluster doubles provide a polynomial-cost approximation that closely reproduces the energies of DOCI, but it breaks down in some cases and, as shown herein, it does not provide particularly good density matrices. In this article, we demonstrate that by using the Jordan–Wigner transformation to turn the seniority zero problem back into a Fermionic one, we can provide mean-field variational results of DOCI quality for the Hubbard model and a few small molecular dissociation examples, with polynomial cost, both for the energies and for density matrices, all while being protected from collapse. This success is rooted in the proof we provide, showing that the Hartree–Fock wave function on the Jordan–Wigner-transformed Hamiltonian transforms back to variational coupled cluster doubles in the seniority zero representation, but restricted to have determinant rather than permanent amplitude coefficients, without compromising its overall accuracy.
Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, in this work, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P 2 C 3 NTs)─obtained by rolling monolayer P 2 C 3 , a two-dimensional material shown in a previous letter to host “double Kagome bands”. Both armchair and zigzag P 2 C 3 NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb–Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb–Kagome to “brick-wall”, accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P 2 C 3 NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.
Identifying experimental probes capable of diagnosing extreme quantum behavior is widely regarded as one of the foremost challenges in modern condensed matter physics. Here, we propose a novel approach for detecting chiral Kitaev spin-liquid states through measurements of the local dynamical spin structure factor on the boundary using scanning tunneling microscopy (STM). We specifically focus on unpaired (“dangling”) Majorana fermions, which naturally emerge along boundaries of Kitaev spin liquids, and can serve as indicators of chiral boundary modes under broad conditions, thereby offering a clear signature of these exotic quantum states.
Altermagnetic (AM) compounds have recently emerged as a promising platform for realizing unconventional quantum phases, enabled by their unique spin-split band structure at zero net magnetization. Here, we present a first-principles investigation of magnetically intercalated transition metal dichalcogenides (TMDs) of the form XY 4 Z 8 (X = Mn, Fe, Co, Ni, Cr, or V; Y = Nb or Ta; and Z = Se or S), identifying a subset of new versatile AM candidates. Our results establish a systematic correlation between interatomic geometry, quantified by the ratio of interlayer to intralayer spacing, and the magnetic ground states. Systems with A-type antiferromagnetic order exhibit momentum-dependent spin splitting consistent with AM behavior. The combination of the AM spin-splitting and the spin-orbit coupling leads to the emergence of Weyl nodes together with the corresponding topological Fermi arc surface states. Moreover, we identify flat bands near the Fermi level that originate from the intercalant-induced formation of an effective kagome-like sublattice in the TMD layer. These results collectively establish magnetically intercalated TMDs as a promising platform for engineering altermagnetism, flat bands, and Weyl fermions within a single material family, facilitating the development of topological and spintronic applications.
Disorders in intermetallic systems belonging to the CeNiSi 2 -family are frequently overlooked. Even compounds presumed to be stoichiometric, such as YFeGe 2 , can be misidentified. Here, in this study, we report a series of Y 4 Fe x Ge 8 (1.0 ≤ x ≤ 1.5) compounds and show, using high-resolution synchrotron X-ray diffraction, that they feature asymmetrical structural distortions in the Fe and Ge sites that lead to a superstructure with partially ordered Fe vacancies and distorted Ge square-net in the triclinic crystal system, space group P[1 with combining macron] with a = 11.4441(3) Å, b = 32.7356(7) Å, c = 11.4456(3) Å, α = 79.6330(10)°, β = 88.3300(10)°, and γ = 79.6350 (10)°. The unit cell is 16 times the conventional orthorhombic cell with the space group Cmcm. We identified the lower and upper limits for Fe in Y 4 Fe x Ge 8 (1.0 ≤ x ≤ 1.5). Our physical property measurements yielded a Sommerfeld coefficient γ = 39.8 mJ mole −1 K −2 , a Kadowaki–Woods ratio of 1.2 × 10 −5 μΩ cm mole 2 K 2 mJ −2 , and a Wilson ratio of 1.83, suggesting heavy fermion behavior in the absence of f electrons, a rather rare case. Furthermore, we observed strong spin frustration and noted findings indicating possible superconductivity associated with the Fe content.
Fermionic dark matter absorption on nuclear targets via neutral current interactions is explored using a nonrelativistic effective field theory framework. An analysis of data from the PICO-60 C 3 F 8 bubble chamber sets leading constraints on spin-independent absorption for dark matter masses below 23 MeV/𝑐 2 and establishes the first limits on spin-dependent absorptive interactions. In conclusion, these results demonstrate the sensitivity of bubble chambers to low-mass dark matter and underscore the importance of absorption searches in expanding the parameter space of direct detection experiments.
Here, we report on magneto-optical trapping of the two fermionic isotopes of atomic titanium, 47 Ti and 49 Ti . Unlike the even mass-number isotopes, which were recently laser cooled, 47 Ti and 49 Ti have nonzero nuclear spins and, consequently, their atomic levels are split by hyperfine structure. Combining and comparing theoretical calculations and atomic beam-spectroscopy measurements, we determine the hyperfine structures and isotope shifts of the 3𝑑 2 4𝑠 2 𝑎 3 𝐹 4 → 3𝑑 2 ( 3 𝑃)4𝑠4𝑝( 3 𝑃 𝑜 ) 𝑦 5 𝐷$^o_4$ optical-pumping transition at optical wavelength 391 nm and the 3𝑑 3 (4𝐹)4𝑠 𝑎 5 𝐹 5 → 3𝑑 3 ( 4 𝐹)4𝑝 𝑦 5 𝐺$^𝑜_6$ laser-cooling transition at wavelength 498 nm. With this information, we produce magneto-optical traps of both 47 Ti and 49 Ti by applying two additional tones of light to repump atoms to the maximum-spin states on the laser-cooling transition. Directly loading from the atomic flux of a titanium sublimation pump, we produce 47 Ti and 49 Ti traps with 731(190) and 1142(240) atoms, and with lifetimes of 330(15) and 310(8) ms, respectively.
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS), which is a central object in quantum statistical mechanics. We introduce several key innovations that significantly improve the practicality and extend the generality of previous techniques. First, our approach allows one to estimate the DOS only for a specific subspace of the full Hilbert space. This is crucial for fermionic systems, since both canonical and grand canonical ensemble thermal equilibrium properties depend on subspaces of fixed number. Second, in our approach, by time evolving very simple, random initial states, such as randomly chosen computational basis states, we can exactly recover the DOS on average. Third, due to circuit-depth limitations, we only reconstruct the DOS up to a convolution with a Gaussian window—thus all imperfections that shift the energy levels by less than the width of the convolution window will not significantly affect the estimated DOS. For these reasons, we find the approach is a promising candidate for early quantum advantage as even short-time, noisy dynamics can yield a semiquantitative reconstruction of the DOS (convolution with a broad Gaussian window), while early fault-tolerant devices will likely enable higher-resolution DOS reconstruction through longer time evolutions. We demonstrate the practicality of our approach in representative Fermi-Hubbard and spin models and indeed find that our approach is highly robust against algorithmic errors in the time evolution and against gate noise. We further demonstrate that our approach is compatible with noisy intermediate-scale quantum (NISQ) computing NISQ-friendly variational techniques, introducing and leveraging a technique for variational time evolution.
The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of 2 × 2 blocks. In each block the possible eigenvalues either form a complex pair or separate into two real eigenvalues that have specific chirality. The collision of these pairs of eigenvalues occurs outside the perturbative region and provides a path between topological sectors.
Motivated by the importance of studying topological superconductors beyond the mean-field approximation, we here investigate mesoscopic islands of time-reversal-invariant topological superconductors. We characterize the spectrum in the presence of strong order-parameter fluctuations in the presence of an arbitrary number of Kramers pairs of Majorana edge states and study the effect of coupling the Coulomb blockaded island to external leads. In the case of an odd fermionic parity on the island, we derive an unconventional Kondo Hamiltonian in which metallic leads couple to both topological Majorana degrees of freedom (which keep track of the parity in different leads) and the overall spin 1 2 in the island. For the simplest case of a single wire (two pairs of Majorana edge states), we demonstrate that anisotropies are irrelevant in the weak coupling renormalization group flow. This permits us to solve the Kondo problem in the vicinity of a Toulouse-type point using Abelian bosonization. We demonstrate a residual ground-state entropy of ln ( 2 ) , which is protected by spin-rotation symmetry, but reduced to ln ( 2 ) (as in the spinless topological Kondo effect) by symmetry-breaking perturbations. In the symmetric case, we further demonstrate the simultaneous presence of both Fermi-liquid and non-Fermi-liquid-like thermodynamics (depending on the observable) and derive charge and spin transport signatures of the Coulomb blockaded island. Published by the American Physical Society 2024