Natanael Costa

Principal component analysis for fermionic critical points

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine

Spiral magnetic phases on the Kondo Lattice Model: A Hartree-Fock approach

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Impurities near an antiferromagnetic-singlet quantum critical point

. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Greens and pair-pair correlation functions.

Ferromagnetism beyond Lieb's theorem

Abstract We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree–Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector Q while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained ‘Doniach-like’ diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic).

Compressible ferrimagnetism in the depleted periodic Anderson model

Heavy fermion systems, and other strongly correlated electron materials, often exhibit a competition between antiferromagnetic (AF) and singlet ground states. Using exact Quantum Monte Carlo (QMC) simulations, we examine the effect of impurities in the vicinity of such AF- singlet quantum critical points, through an appropriately defined impurity susceptibility,

A mean-field approach to Kondo-attractive-Hubbard model

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Effect of phonon dispersion on the competition between pairing and charge order

. Our key finding is a connection, within a single calculational framework, between AF domains induced on the singlet side of the transition, and the behavior of the nuclear magnetic resonance (NMR) relaxation rate

Coexistence between magnetism and superconductivity within the Kondo--attractive-Hubbard model: the borocarbides as a case study

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A mean field study of quantum transitions in a spin-1/2 XY chain with a transverse long-range interaction

. We show that local NMR measurements provide a diagnostic for the location of the QCP which agrees remarkably well with the vanishing of the AF order parameter and large values of

Impurities near an Antiferromagnetic-Singlet Quantum Critical Point

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