Fractionalization and Fermi surface volume in heavy fermion compounds: the case of YbRh2_2 Si2_2

We establish an effective theory for heavy fermion compounds close to a zero temperature Anti-Ferromagnetic (AF) transition. Coming from the heavy Fermi liquid phase across to the AF phase, the heavy electron fractionalizes into a light electron, a bosonic spinon and a {\it new} excitation: a spinless fermionic field. Assuming this field acquires dynamics and dispersion when one integrates out the high energy degrees of freedom, we give a scenario for the volume of its Fermi surface through the phase diagram. We apply our theory to the special case of YbRh$_2$(Si$_{1-x}$ Ge$_x$)$_2$ where we recover, within experimental resolution, several low temperature exponents for transport and thermodynamics.Comment: 4 pages, 5 figure

Kondo Breakdown as a Selective Mott Transition in the Anderson Lattice

We show within the slave boson technique, that the Anderson lattice model exhibits a Kondo breakdown quantum critical point (KB-QCP) where the hybridization goes to zero at zero temper- ature. At this fixed point, the f-electrons experience as well a selective Mott transition separating a local-moment phase from a Kondo-screened phase. The presence of a multi-scale QCP in the An- derson lattice in the absence of magnetism is discussed in the context of heavy fermion compounds. This study is the first evidence for a selective Mott transition in the Anderson lattice.Comment: 4 pages, 2 figures, version with new figures and typos correcte

Critical phenomena near the antiferromagnetic quantum critical point of Heavy-Fermions

We present a study of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S=1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction which allows one to treat the spin fluctuations and the Kondo effect on an equal footing. The calculations, developed in a self-consistent one-loop approximation, lead to the formation of a damped collective mode with a dynamic exponent z=2 in the case of an antiferromagnetic instability. The system displays a quantum-classical crossover at finite temperature depending how the energy of the mode, on the scale of the magnetic correlation length, compares to k_B T. The low temperature behavior, in the different regimes separated by the crossover temperatures, is then discussed for both 2- and 3-dimensional systems.Comment: 24 pages, 5 figures, added reference

The phase diagram of the underdoped cuprates at high magnetic field

The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives way to a long-range charge order with increasing magnetic field; both the orders coexist in a small intermediate region. The charge order transition is strikingly insensitive to temperature, and quickly reaches a transition temperature close to the zero-field superconducting $T_c$. We argue that such a transition along with the presence of the coexisting phase cannot be described simply by a competing orders formalism. We demonstrate that for some range of parameters there is an enlarged symmetry of the strongly coupled charge and superconducting orders in the system depending on their relative masses and the coupling strength of the two orders. We establish that this sharp switch from the superconducting phase to the charge order phase can be understood in the framework of a composite SU(2) order parameter comprising the charge and superconducting orders. Finally, we illustrate that there is a possibility of the coexisting phase of the competing charge and superconducting orders only when the SU(2) symmetry between them is weakly broken due to biquadratic terms in the free energy. The relation of this sharp transition to the proximity to the pseudogap quantum critical doping is also discussed

Collective mode in the SU(2) theory of cuprates

Recent advances in momentum-resolved electron energy-loss spectroscopy (MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to access the charge response function with unprecedented versatility and accuracy. This allows for the study of excitations which were inaccessible recently, such as low-energy and finite momentum collective modes. The SU(2) theory of the cuprates is based on a composite order parameter with SU(2) symmetry fluctuating between superconductivity and charge order. The phase where it fluctuates is a candidate for the pseudogap phase of the cuprates. This theory has a signature, enabling its strict experimental test, which is the fluctuation between these two orders, corresponding to a charge 2 spin 0 mode at the charge ordering wave-vector. Here we derive the influence of this SU(2) collective mode on the charge susceptibility in both strong and weak coupling limits, and discuss its relation to MEELS, RIXS and Raman experiments. We find two peaks in the charge susceptibility at finite energy, whose middle is the charge ordering wave-vector, and discuss their evolution in the phase diagram

Angle Resolved Photo-Emission Spectroscopy signature of the Resonant Excitonic State

We calculate the Angle Resolved PhotoEmission Spectroscopy (ARPES) signature of the Resonant Excitonic State (RES) that was proposed as the Pseudo-Gap state of cuprate superconductors [ArXiv 1510.03038]. This new state can be described as a set of excitonic (particle-hole) patches with an internal checkerboard modulation. Here, we modelize the RES as a charge order with $\bf{2p_{F}}$ wave vectors, where $\bf{2p_{F}}$ is the ordering vector connecting two opposite sides of the Fermi surface. We calculate the spectral weight and the density of states in the RES and we find that our model correctly reproduces the opening of the PG in Bi-2201

Deterministic elliptic curve primality proving for a special sequence of numbers

We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm uses O(log N) arithmetic operations in the ring Z/NZ, implying a bit complexity that is quasi-quadratic in log N. Notably, neither of the classical "N-1" or "N+1" primality tests apply to the integers in our sequence. We discuss how this algorithm may be applied, in combination with sieving techniques, to efficiently search for very large primes. This has allowed us to prove the primality of several integers with more than 100,000 decimal digits, the largest of which has more than a million bits in its binary representation. At the time it was found, it was the largest proven prime N for which no significant partial factorization of N-1 or N+1 is known.Comment: 16 pages, corrected a minor sign error in 5.

Model of Quantum Criticality in He3 bilayers Adsorbed on graphite

Recent experiments on He3 bilayers adsorbed on Graphite have shown striking quantum critical properties at the point where the first layer localizes. We model this system with the Anderson lattice plus inter-layer Coulomb repulsion in two dimensions. Assuming that quantum critical fluctuations come from a vanishing of the effective hybridization, we can reproduce several features of the system, including the apparent occurrence of two quantum critical points (QCP), the variation of the effective mass and coherence temperature with coverage.Comment: 4 pages, 2 figures, new version as published on PRL, journal reference and DOI adde

SU(2)-symmetry in a realistic spin-fermion model for cuprate superconductors

We consider the Pseudo-Gap (PG) state of high-$T_c$ superconductors in form of a composite order parameter fluctuating between 2$p_F$-charge ordering and superconducting (SC) pairing. In the limit of linear dispersion and at the hotspots, both order parameters are related by a SU(2) symmetry and the eight hotspot model of Efetov $\textit{et al.}$ [Nat. Phys. $\bf{9}$, 442 (2013)] is recovered. In the general case however, curvature terms of the dispersion will break this symmetry and the degeneracy between both states is lifted. Taking the full momentum dependence of the order parameter into account, we measure the strength of this SU(2) symmetry breaking over the full Brillouin zone. For realistic dispersion relations including curvature we find generically that the SU(2) symmetry breaking is small and robust to the fermiology and that the symmetric situation is restored in the large paramagnon mass and coupling limit. Comparing the level splitting for different materials we propose a scenario that could account for the competition between the PG and the SC states in the phase diagram of high-$T_c$ superconductors.Comment: 6 pages, 7 figures, published versio