arXiv subjects

A. -M. S. Tremblay

Publications and source records attributed to A. -M. S. Tremblay.

At least 109 records · Page 6Linked to original sources

arXiv2009

Pairing dynamics in strongly correlated superconductivity

Confirmation of the phononic origin of Cooper pair formation in superconductors came with the demonstration that the interaction was retarded and that the corresponding energy scales were associated with phonons. Using cellular dynamical mean-field theory for the two-dimensional Hubbard model, we identify such retardation effects in d-wave pairing and associate the corresponding energy scales with short-range spin fluctuations. We find which frequencies are relevant for pairing as a function of interaction strength and doping and show that the disappearance of superconductivity on the overdoped side coincides with the disappearance of the low energy feature in the antiferromagnetic fluctuations, as observed in neutron scattering experiments.

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arXiv2008

Spin-Josephson effect in antiferromagnetic tunnel junctions

In the Josephson effect, coherent Cooper pair tunneling is driven by the phase difference between the superconducting order parameters on opposite sides of the junction. By analogy, differences in order parameters across a junction should lead to coherent tunneling of the condensed objects that exist in the broken symmetry state. To exhibit the generality of this phenomenon and make predictions from a realistic model, we study the case of a tunnel junction between two itinerant antiferromagnets. At the mean-field level, we find an equilibrium current of the staggered magnetization through the junction that is proportional the normal state conductance and to $\mathbf{S}_{L}\times \mathbf{S}_{R}$ where $\mathbf{S}_{L}$ and $\mathbf{S}_{R}$ are the staggered magnetizations on either sides. Microscopically, this effect comes from coherent tunneling of spin-one charge-zero particle-hole pairs that have a net wave vector equal to the antiferromagnetic one. We explain similarities and differences with the standard DC and AC Josephson effects.

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arXiv2008

First order Mott transition at zero temperature in two dimensions: Variational plaquette study

The nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first order transition is expected to profoundly influence the nature of the finite temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature.

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arXiv2008

Scaling and commensurate-incommensurate crossover for the d=2, z=2 quantum critical point of itinerant antiferromagnets

Quantum critical points exist at zero temperature, yet, experimentally their influence seems to extend over a large part of the phase diagram of systems such as heavy-fermion compounds and high-temperature superconductors. Theoretically, however, it is generally not known over what range of parameters the physics is governed by the quantum critical point. We answer this question for the spin-density wave to fermi-liquid quantum critical point in the two-dimensional Hubbard model. This problem is in the $d=2,z=2$ universality class. We use the Two-Particle Self-Consistent approach, which is accurate from weak to intermediate coupling, and whose critical behavior is the same as for the self-consistent-renormalized approach of Moriya. Despite the presence of logarithmic corrections, numerical results demonstrate that quantum critical scaling for the static magnetic susceptibility can extend up to very high temperatures but that the commensurate to incommensurate crossover leads to deviations to scaling.

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arXiv2008

Low energy theory of the t-t'-t''-U Hubbard Model at half-filling: interaction strengths in cuprate superconductors and an effective spin-only description of La_2CuO_4

Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many new types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band structure calculations and photoemission experiments on these systems, we include second and third neighbor hopping parameters, t' and t'', into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed, four hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4. Performing a spin wave analysis, we calculate the magnon dispersion as a function of U,t,t' and t''. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377, {2001}] for La2CuO4. The ring exchange terms are found essential, in particular to determine the relative sign of t' and t'', with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength U~8t consistent with Mott insulating behavior.

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arXiv2008

Competition between charge and spin order in the $t-U-V$ extended Hubbard model on the triangular lattice

Several new classes of compounds can be modeled in first approximation by electrons on the triangular lattice that interact through on-site repulsion $U$ as well as nearest-neighbor repulsion $V$. This extended Hubbard model on a triangular lattice has been studied mostly in the strong coupling limit for only a few types of instabilities. Using the extended two-particle self consistent approach (ETPSC), that is valid at weak to intermediate coupling, we present an unbiased study of the density and interaction dependent crossover diagram for spin and charge density wave instabilities of the normal state at arbitrary wave vector. When $U$ dominates over $V$ and electron filling is large, instabilities are chiefly in the spin sector and are controlled mostly by Fermi surface properties. Increasing $V$ eventually leads to charge instabilities. In the latter case, it is mostly the wave vector dependence of the vertex that determines the wave vector of the instability rather than Fermi surface properties. At small filling, non-trivial instabilities appear only beyond the weak coupling limit. There again, charge density wave instabilities are favored over a wide range of dopings by large $V$ at wave vectors corresponding to $\sqrt(3) \times \sqrt(3)$ superlattice in real space. Commensurate fillings do not play a special role for this instability. Increasing $U$ leads to competition with ferromagnetism. At negative values of $U$ or $V$, neglecting superconducting fluctuations, one finds that charge instabilities are favored. In general, the crossover diagram presents a rich variety of instabilities. We also show that thermal charge-density wave fluctuations in the renormalized classical regime can open a pseudogap in the single-particle spectral weight, just as spin or superconducting fluctuations.

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arXiv2007

Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step towards a quantitative theory of the competition between antiferromagnetism (AFM) and d-wave superconductivity (SC) in the cuprates, we use Cellular Dynamical Mean Field Theory to compute zero temperature properties of the two-dimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second-neighbor hopping t', the zero temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third-neighbor hopping t'' improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs T_{c}/T_{c}^{max} phase diagram of the cuprates is universal. The calculated ARPES spectrum displays the observed electron-hole asymmetry. Our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard BCS approach.

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arXiv2007

Conditions for magnetically induced singlet d-wave superconductivity on the square lattice

It is expected that at weak to intermediate coupling, d-wave superconductivity can be induced by antiferromagnetic fluctuations. However, one needs to clarify the role of Fermi surface topology, density of states, pseudogap, and wave vector of the magnetic fluctuations on the nature and strength of the induced d-wave state. To this end, we study the generalized phase diagram of the two-dimensional half-filled Hubbard model as a function of interaction strength $U/t$, frustration induced by second-order hopping $t^{\prime}/t$, and temperature $T/t$. In experiment, $U/t$ and $t^{\prime}/t$ can be controlled by pressure. We use the two-particle self-consistent approach (TPSC), valid from weak to intermediate coupling. We first calculate as a function of $t^{\prime}/t$ and $U/t$ the temperature and wave vector at which the spin response function begins to grow exponentially.D-wave superconductivity in a half-filled band can be induced by such magnetic fluctuations at weak to intermediate coupling, but only if they are near commensurate wave vectors and not too close to perfect nesting conditions where the pseudogap becomes detrimental to superconductivity. For given $U/t$ there is thus an optimal value of frustration $t^{\prime}/t$ where the superconducting $T_c$ is maximum. The non-interacting density of states plays little role. The symmetry d$_{x^{2}-y^{2}}$ vs d$_{xy}$ of the superconducting order parameter depends on the wave vector of the underlying magnetic fluctuations in a way that can be understood qualitatively from simple arguments.

cond-mat.str-el↗

arXiv2007

Magnetism and d-wave superconductivity on the half-filled square lattice with frustration

The role of frustration and interaction strength on the half-filled Hubbard model is studied on the square lattice with nearest and next-nearest neighbour hoppings t and t' using the Variational Cluster Approximation (VCA). At half-filling, we find two phases with long-range antiferromagnetic (AF) order: the usual Neel phase, stable at small frustration t'/t, and the so-called collinear (or super-antiferromagnet) phase with ordering wave-vector $(π,0)$ or $(0,π)$, stable for large frustration. These are separated by a phase with no detectable long-range magnetic order. We also find the d-wave superconducting (SC) phase ($d_{x^2-y^2}$), which is favoured by frustration if it is not too large. Intriguingly, there is a broad region of coexistence where both AF and SC order parameters have non-zero values. In addition, the physics of the metal-insulator transition in the normal state is analyzed. The results obtained with the help of the VCA method are compared with the large-U expansion of the Hubbard model and known results for the frustrated J1-J2 Heisenberg model. These results are relevant for pressure studies of undoped parents of the high-temperature superconductors: we predict that an insulator to d-wave SC transition may appear under pressure.

cond-mat.str-el↗

arXiv2007

Supersolidity, entropy and frustration

We study the properties of t-t'-V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t-V model where the supersolid characterized by the ordering pattern (x,x,-2x') ("ferrimagnetic" or SS A) is a ground state for chemical potential μ>3V. By turning on either temperature or t' at half-filling μ=3V, we find a first order transition from SS A to the elusive supersolid characterized by the (x,-x,0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a large region where a superfluid phase becomes a solid upon raising temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.

cond-mat.str-el↗

arXiv2007

Convexity of the self-energy functional in the variational cluster approximation

In the variational cluster approximation (VCA) (or variational cluster perturbation theory), widely used to study the Hubbard model, a fundamental problem that renders variational solutions difficult in practice is its known lack of convexity at stationary points, i.e. the physical solutions can be saddle points rather than extrema of the self-energy functional. Here we suggest two different approaches to construct a convex functional of the self-energy. In the first approach, one can show analytically that in the approximation where the irreducible particle-hole vertex depends only on center of mass coordinates, the functional is convex away from phase transitions in the corresponding channel. Numerical tests on a tractable version of that functional show that convexity can be a nuisance when looking for instabilities both in the pairing and particle-hole channels. Therefore, an alternative phenomenological functional is proposed. Convexity is explicitly enforced only with respect to a restricted set of variables, such as the cluster chemical potential that is known to be otherwise problematic. Numerical tests show that our functional is convex at the physical solutions of VCA and allows second-order phase transitions in the pairing channel as well. This opens the way to the use of more efficient algorithms to find solutions of the VCA equations.

cond-mat.str-el↗

arXiv2007

Interaction-Induced Adiabatic Cooling for Antiferromagnetism in Optical Lattices

In the experimental context of cold-fermion optical lattices, we discuss the possibilities to approach the pseudogap or ordered phases by manipulating the scattering length or the strength of the laser-induced lattice potential. Using the Two-Particle Self-Consistent Approach as well as Quantum Monte Carlo simulations, we provide isentropic curves for the two- and three-dimensional Hubbard models at half-filling. These quantitative results are important for practical attempts to reach the ordered antiferromagnetic phase in experiments on optical lattices of two-component fermions. We find that adiabatically turning on the interaction in two dimensions to cool the system is not very effective. In three dimensions, adiabatic cooling to the antiferromagnetic phase can be achieved in such a manner although the cooling efficiency is not as high as initially suggested by Dynamical Mean-Field Theory. Adiabatic cooling by turning off the repulsion beginning at strong coupling is possible in certain cases.

cond-mat.str-el↗

arXiv2007

Non-Perturbative Treatment of Charge and Spin Fluctuations in the Two-Dimensional Extended Hubbard Model: Extended Two-Particle Self-Consistent Approach

We study the spin and charge fluctuations of the extended Hubbard model (EHM) with on-site interaction U and first neighbor interaction V on the two-dimensional square lattice in the weak to intermediate coupling regime. We propose an extension of the two-particle self-consistent (ETPSC) approximation that includes the effect of functional derivatives of the pair correlation functions on irreducible spin and charge vertices. These functional derivatives were ignored in our previous work. We evaluate them assuming particle-hole symmetry. The resulting theory satisfies conservations laws and the Mermin-Wagner theorem. Our current results are in much better agreement with benchmark Quantum Monte-Carlo (QMC) results. As a function of U and V, we can determine the crossover temperatures towards renormalized classical regimes where either spin or charge fluctuations dominate. The dominant wave vector is self-determined by the approach.

cond-mat.str-el↗

arXiv2006

Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors

We study the Mott transition, antiferromagnetism and superconductivity in layered organic conductors using Cellular Dynamical Mean Field Theory for the frustrated Hubbard model. A d-wave superconducting phase appears between an antiferromagnetic insulator and a metal for $t^{\prime}/t=0.3-0.7 $, or between a nonmagnetic Mott insulator (spin liquid) and a metal for $t^{\prime}/t\geq 0.8$, in agreement with experiments on layered organic conductors including $κ$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$. These phases are separated by a strong first order transition. The phase diagram gives much insight into the mechanism for d-wave superconductivity. Two predictions are made.

cond-mat.str-el↗

arXiv2006

Potential-energy (BCS) to kinetic-energy (BEC)-driven pairing in the attractive Hubbard model

The BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For $U$ smaller than the bandwidth, pairing is driven by the potential energy, while in the opposite case it is driven by the kinetic energy, resembling a recent optical conductivity experiment in cuprates. Phase coherence leads to the appearance of a collective Bogoliubov mode in the density-density correlation function and to the sharpening of the spectral function.

cond-mat.str-el↗

arXiv2006

Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory

We study the Hubbard model using the Cellular Dynamical Mean-Field Theory (CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic details of CDMFT with the Hirsch-Fye QMC method for the solution of the self-consistently embedded quantum cluster problem. We use the one- and two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC particularly for small clusters by comparing with the exact results and also with other quantum cluster methods. We calculate single-particle Green's functions and self-energies on small clusters to study their size dependence in one- and two-dimensions.

cond-mat.str-el↗

arXiv2006

Pseudogap induced by short-range spin correlations in a doped Mott insulator

We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the Cellular Dynamical Mean Field Theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.

cond-mat.str-el↗

arXiv2006

Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory

This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments has been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the Two-Particle Self-Consistent Approach, Variational Cluster Perturbation Theory (or variational cluster approximation), and Cellular Dynamical Mean-Field Theory.

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