Spin-fermion mappings for even Hamiltonian operators

We revisit the Jordan-Wigner transformation, showing that --rather than a non-local isomorphism between different fermionic and spin Hamiltonian operators-- it can be viewed in terms of local identities relating different realizations of projection operators. The construction works for arbitrary dimension of the ambient lattice, as well as of the on-site vector space, generalizing Jordan-Wigner's result. It provides direct mapping of local quantum spin problems into local fermionic problems (and viceversa), under the (rather physical) requirement that the latter are described by Hamiltonian's which are even products of fermionic operators. As an application, we specialize to mappings between constrained-fermions models and spin 1 models on chains, obtaining in particular some new integrable spin Hamiltonian, and the corresponding ground state energies.Comment: 7 pages, ReVTeX file, no figure

Hubbard model on triangular N -leg cylinders: Chiral and nonchiral spin liquids

The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Phys. Rev. X 10, 021042 (2020)10.1103/PhysRevX.10.021042]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider N-leg cylinders. For N=4 and in the presence of a next-nearest-neighbor hopping, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for both N=5 and 6, the chiral spin liquid is not the state with the lowest variational energy: in the former case, a nematic spin liquid is found in the entire insulating regime, while for the less frustrated case with N=6 the results are very similar to that obtained on two-dimensional clusters [L. F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B 102, 115150 (2020)2469-995010.1103/PhysRevB.102.115150], with an antiferromagnetic phase close to the metal-insulator transition and a nematic spin liquid in the strong-coupling regime

Magnetic and spin-liquid phases in the frustrated t-t′ Hubbard model on the triangular lattice

The Hubbard model and its strong-coupling version, the Heisenberg one, have been widely studied on the triangular lattice to capture the essential low-temperature properties of different materials. One example is given by transition metal dichalcogenides, as 1T-TaS$_2$, where a large unit cell with 13 Ta atoms forms weakly coupled layers with an isotropic triangular lattice. By using accurate variational Monte Carlo calculations, we report the phase diagram of the $t-t′$ Hubbard model on the triangular lattice, highlighting the differences between positive and negative values of $t′/t$; this result can be captured only by including the charge fluctuations that are always present for a finite electron-electron repulsion. Two spin-liquid regions are detected: one for $t′/t0$. The spin-liquid phase appears to be gapless, though the variational wave function has a nematic character, in contrast to the Heisenberg limit. We do not find any evidence for nonmagnetic Mott phases in the proximity of the metal-insulator transition, at variance with the predictions (mainly based upon strong-coupling expansions in $t/U$) that suggest the existence of a weak-Mott phase that intrudes between the metal and the magnetically ordered insulator

Hubbard model on triangular N-leg cylinders: Chiral and nonchiral spin liquids

The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Phys. Rev. X 021042 (2020)]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider N-leg cylinders. For N = 4 and in the presence of a next-nearest-neighbor hopping, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for both N = 5 and 6, the chiral spin liquid is not the state with the lowest variational energy: in the former case, a nematic spin liquid is found in the entire insulating regime, while for the less frustrated case with N = 6 the results are very similar to that obtained on two-dimensional clusters [L. F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B 102, 115150 (2020)], with an antiferromagnetic phase close to the metal-insulator transition and a nematic spin liquid in the strong-coupling regime

Development of a Numerical Approach for the CFD Simulation of a Gear Pump under Actual Operating Conditions

The geometric complexity and high-pressure gradients that characterize the design of the flow field of gear pumps make it very difficult to obtain an accurate CFD simulation of the component. Usually, assumptions are made both in terms of geometrical features and physics being included in the analysis. The contact between the teeth, which is a key factor for the correct functioning of these pumps, represents a critical challenge in 3D CFD simulations, mainly due to the intrinsic limits of the dynamic meshing techniques that can hardly effectively manage a zero or close to zero gap point forming during gear rotation. The geometric complexity and high-pressure gradients that characterize the gear pump flow field make a CFD analysis quite difficult, and the contact between the gear teeth is usually avoided, thus being an extremely important feature. In this paper, a gear pump composed of inlet and outlet pipes was considered, and the contact between the gear's teeth was modeled in two different ways, one where it is effectively implemented and one where it is avoided using distancing and a proper casing modification. Herein, a new methodology is proposed for the application of the dynamic mesh method in the Simcenter STAR-CCM+ environment using an adaptive remeshing technique. The proposed methodology is compared with the alternative overset meshing method available in the software. The new meshing method is implemented using a user-routing that reproduces the real geometry of the gears while rotating during the pump operation, with teeth contact included. The routine is optimized in order to limit the additional computation and time needed for the remeshing process. The results that can be obtained using the two meshing approaches for the gear pump are compared in terms of computational effort and the accuracy of the results. The two methods showed opposite results in almost all the reported results, with the overset being more precise in the radial pressure evaluation and the dynamic being more reliable in the cavitation/aeration extension cloud

A Computation Fluid Dynamics Methodology for the Analysis of the Slipper-Swash Plate Dynamic Interaction in Axial Piston Pumps

This paper proposes a CFD methodology for the simulation of the slipper's dynamics of a swash-plate axial piston unit under actual operating conditions. The study considers a typical slipper design, including a vented groove at the swash-plate interface. The dynamic fluid-body interaction (DFBI) model is exploited to find the instantaneous position of the slipper, while the morphing approach is adopted to cope with the corresponding mesh distortion. A modular approach is adopted to ensure high-quality mesh on the entire slipper surface and sliding interfaces provide the fluid dynamic connection between neighboring regions. The external forces acting on the slipper are included by means of user-defined lookup tables with the simulation estimating the lift force induced by fluid compression. Moreover, the force produced by the metal-to-metal contact between the slipper and the swash plate is modeled through a specific tool of the software. The pressure signal over an entire revolution of the pump is taken as an input of the simulation and a variable time step is used to manage the high-pressure gradients occurring in the regions of inner and outer dead points of the piston. The weakly compressible characteristic of the fluid is considered by a specific pressure-dependent density approach, and the two-equation eddy-viscosity k-omega SST (shear stress transport) model is used to assess the turbulent behavior of the flow. Furthermore, the transitional model predicts the onset of transition, thus solving different equations depending on whether the flow enters a laminar or turbulent regime. In conclusion, the proposed methodology investigates the motion of the slipper in response to several external forces acting on the component. The numerical results are discussed in terms of variable clearance height, pressure distribution within the gap, and lift forces acting on the slipper under specific pump operations