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Factor cluster formalisms in many fermion theory development, discussing primitive decomposition equations rearrangements and linked cluster theorem validity
N representability problem for first and second order density matrices for odd number of fermions
A linearized version of the Hartree-Fock method is used as a probe to investigate phase transitions in fermionic systems with many-body interactions. An application to a new exactly solvable model which includes two- and three-body forces is shown.
From the decomposition of the exceptional Lie algebras (ELA's) under a maximal unitary subalgebra a realization of the ELA's is obtained in terms of fermionic oscillators.
Dual evaporation gives 50 million fermions at T = 0.1 T(sub F). Demonstrated suppression of interactions by coherent superposition - applicable to atomic clocks. Looking for evidence of Cooper pairing and superfluidity.
Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. Here, in this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalised single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.
Here, by utilizing a multiorbital periodic Anderson model with parameters obtained from ab initio band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both nonmagnetic 4𝑓 0 and magnetic 4𝑓 2 virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn 3 . The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of 4𝑓 materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.
Scalar leptoquarks (LQ) with masses between 2 TeV and 50 TeV are prime candidates to explain deviations between measurements and Standard-Model predictions in decay observables of b-flavored hadrons (“flavor anomalies”). Explanations of low-energy data often involve $\mathcal{O}$ (1) LQ-quark-lepton Yukawa couplings, especially when collider bounds enforce a large LQ mass. This calls for the calculation of radiative corrections involving these couplings. Studying such corrections to LQ-mediated b → cτν and b → sℓ + ℓ − amplitudes, we find that they can be absorbed into finite renormalizations of the LQ Yukawa couplings. If one wants to use Yukawa couplings extracted from low-energy data for the prediction of on-shell LQ decay rates, one must convert the low-energy couplings to their high-energy counterparts, which subsume the corrections to the on-shell LQ-quark-lepton vertex. We present compact formulae for these correction factors and find that in scenarios with S 1 , R 2 , or S 3 LQ the high-energy coupling is always smaller than the low-energy one, which weakens the impact of collider data on the determination of the allowed parameter spaces. For the R 2 scenario addressing b → cτν, in which one of the two involved Yukawa coupling must be significantly larger than 1, we find this coupling reduced by 15% at high energy. If both S 1 and R 2 are present, the high-energy coupling can also be larger and the size of the correction is unbounded, because tree contribution and vertex corrections involve different couplings. We further present the conversion formula to the $\overline{MS}$ scheme for the Yukawa couplings of the S 3 scenario.
To overcome the limitations of existing algorithms for solving self-bound quantum many-body problems—such as those encountered in nuclear and particle physics—that access only a restricted subset of energy levels and provide limited structural information, we introduce and demonstrate a novel quantum-classical approach capable of resolving the complete bound-state spectrum. This method also provides the total angular momentum 𝐽 associated with each eigenstate. Here, our approach is based on expressing the Hamiltonian in second-quantized form within a novel input model combined with a scan scheme, enabling broad applicability to configuration-interaction calculations across diverse fields. We apply this hybrid method to compute, for the first time, the bound-state spectrum together with corresponding 𝐽 values of 20 O using a realistic strong-interaction Hamiltonian. Our approach applies to hadron spectra and 𝐽 values solved in the relativistic basis light-front quantization approach.
Exotic electronic physics including correlated insulating states and fractional Chern insulators have been observed in twisted bilayer graphene in a magnetic field when the Fermi velocity vanishes; however, a question remains as to the stability of these states, which is controlled by the gap to the first excited state. Free-space terahertz magneto-optics can directly probe the gap to charge excitations, which bounds the stability of electronic states, but this measurement has thus far been inaccessible due to the micron size of twisted bilayer graphene samples, while the wavelength of terahertz light is up to 1 mm. Here we leverage advances in fabrication to create twisted bilayer graphene samples over 5×5 mm in size with a uniform twist angle and study the magnetic field dependence of the cyclotron resonance by a complex Faraday rotation experiment in 𝑝-doped large angle twisted bilayer graphene. These measurements directly probe charge excitations in inter-Landau level transitions and determine the Fermi velocity as a function of twist angle.
We present lattice results for the flavor diagonal charges of the proton from the analysis of eight ensembles generated using 2+1+1-flavors of highly improved staggered quarks by the MILC Collaboration. The calculation includes all the needed connected and disconnected contributions to nucleon three-point function. For extracting matrix elements using fits to the spectral decomposition of these correlation functions, two strategies to remove excited state contributions are employed and compared. To renormalize these charges, the 2+1-flavor mixing matrix is calculated in the regularization independent symmetric momentum subtraction intermediate scheme on the lattice. The final results are presented in the $\overline{MS}$ scheme at scale 2 GeV. The axial charges for the proton are $𝑔$$^{𝑢}_{𝐴}$ = 0.781(25), $𝑔$$^{𝑑}_{𝐴}$ =−0.440(39), and $𝑔$$^{𝑠}_{𝐴}$ = −0.055(9); the tensor charges are $𝑔$$^{𝑢}_{𝑇}$ = 0.782(28), $𝑔$$^{𝑑}_{𝑇}$ = −0.195(16), and $𝑔$$^{𝑠}_{𝑇}$ = −0.0016(12); and the scalar charges are $𝑔$$^{𝑢}_{𝑆}$ = 9.39(88), $𝑔$$^{𝑑}_{𝑆}$ = 8.84(93), and $𝑔$$^{𝑠}_{𝑆}$ = 0.37(14). Results for the neutron are given by the 𝑢 ↔ 𝑑 interchange. Results for the sigma terms are 𝜎 𝜋𝑁 | standard = 42(6) MeV from a “standard” analysis and 𝜎 𝜋𝑁 | 𝑁𝜋 = 61(6) MeV from an “𝑁𝜋” analysis that includes the contributions of multihadron 𝑁𝜋 excited states as motivated by chiral perturbation theory. Our preferred value 𝜎 𝜋𝑁 | 𝑁𝜋 is consistent with the phenomenological extraction from 𝜋 −𝑁 scattering data. The strangeness content of the proton, for which the standard analysis is appropriate, is 𝜎 𝑠 | standard = 35(13) MeV.
The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Nonrelativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain nonrelativistic Breit frame densities.
CeRh 2 As 2 is rare among superconductors, in that the magnetic field tunes it between two distinct superconducting phases. Combined with a lack of local inversion symmetry and an upper critical field exceeding the Pauli paramagnetic limit, this excitingly suggests triplet multicomponent superconductivity. Preceding the superconducting onset, 𝑓-electron correlations cause long-range order, attributed both to local antiferromagnetism and itinerant (quadrupole) density waves. A magnetic field provides a significant perturbation of the 𝑓 electrons and may reveal the nature of the many-body correlations. Therefore, we report comprehensive magnetization and magnetotransport studies on microstructured devices in fields of up to 73 T. Applied along the 𝑐 axis, the field causes a low-temperature change of majority (hole) carrier density at 𝜇 0 𝐻 ≈ 24 T. By contrast, in-plane fields produce a cascade of phase transitions; the field-induced in-plane conductivity anisotropy and lack of accompanying magnetic features, plus the closed-dome nature of the overall phase boundary is consistent with a hierarchy of field-induced density-wave states.