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S. Moukouri

Publications and source records attributed to S. Moukouri.

At least 19 recordsLinked to original sources
arXiv2012

On the universality class of the Mott transition in two dimensions

We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a non-perfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi one-dimensional modeldisplays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be $ν\approx 1.0$. This implies that the fermionic Mott transition, belongs to the universality class of the 2D Ising model. The Mott insulator is the 'ordered' phase whose order parameter is given by the density of singly occupied sites minus that of holes and doubly occupied sites.

cond-mat.str-el↗
arXiv2011

Mott Transition in Quasi-One-Dimensional Systems

We report the application of the density-matrix renormalization group method to a spatially anisotropic two-dimensional Hubbard model at half-filling. We find a deconfinement transition induced by the transverse hopping parameter $t_y$ from an insulator to a metal. Therefore, if $t_y$ is fixed in the metallic phase, increasing the interaction $U$ leads to a metal-to-insulator transition at a finite critical $U$. This is in contrast to the weak-coupling Hartree-Fock theory which predicts a nesting induced antiferromagnetic insulator for any $U>0$.

cond-mat.str-el↗
arXiv2011

Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model

The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.

cond-mat.str-el↗
arXiv2010

A two-step density-matrix renormalization-group study of coupled Luttinger liquids

We report a two-step density-matrix renormalization-group computation of the equal-time single-particle Green's function, the density-density correlations, and the low-frequency spectral weight function of a spinless fermion model in an anisotropic two-dimensional lattice at half-filling. We find that at weak couplings the density-density correlations have the universal decay of a Fermi liquid; the spectral weight function displays a sharp quasi-particle peak. But in the vicinity of a quantum critical point, these correlations strongly deviate from a Fermi liquid prediction and a pseudogap opens in the spectral weight function.

cond-mat.str-el↗
arXiv2008

The Plaquette Ground State of the Shastry-Sutherland Model

I use the two-step density-matrix renormalization group method based on two-leg ladder expansion to show numerical evidence of a plaquette ground state for $J_2=1.3J_1$ in the Shastry-Sutherland model. I argue that the DMRG method is very efficient in the strong frustration regime of two-dimensional spin models where a spin-Peierls ground state is expected to occur. It is thus complementary to quantum Monte Carlo algorithms, which are known to work well in the small frustration regime but which are plagued by the sign problem in the strong frustration regime.

cond-mat.str-el↗
arXiv2007

Néel and Valence-Bond Crystal phases of the Two-Dimensional Heisenberg Model on the Checkerboard Lattice

I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as $J_2$ increases are: (i) Néel with $Q=(π,π)$, (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with $Q=(π/2,π)$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point $J_2=J_1$, the ground state is made of weakly interacting plaquettes with a large gap $Δ\approx 0.67 J_1$ to triplet excitations.

cond-mat.str-el↗
arXiv2007

Antiferromagnetism and Superconductivity in a model of Quasi 1D Organic Conductors

I apply a two-step renormalization group method to the study of the competition between antiferromagnetism (AFM) and superconductivity in an anisotropic 2D Hubbard model. I show that this simple model captures the essentials of the ground-state phases of the quasi 1D organic conductors. As found experimentally, the ground-state phase diagram is mostly AFM. The AFM is localized in the strong-coupling limit where the electrons are confined in the chains. It is an SDW in the weak-coupling limit where interchain hopping is present. There is a tiny region in the weak-coupling regime where transverse two-particle hopping is dominant over magnetism.

cond-mat.str-el↗
arXiv2007

A Renormalization group approach for highly anisotropic 2D Fermion systems: application to coupled Hubbard chains

I apply a two-step density-matrix renormalization group method to the anisotropic two-dimensional Hubbard model. As a prelude to this study, I compare the numerical results to the exact one for the tight-binding model. I find a ground-state energy which agrees with the exact value up to four digits for systems as large as $24 \times 25$. I then apply the method to the interacting case. I find that for strong Hubbard interaction, the ground-state is dominated by magnetic correlations. These correlations are robust even in the presence of strong frustration. Interchain pair tunneling is negligible in the singlet and triplet channels and it is not enhanced by frustration. For weak Hubbard couplings, interchain non-local singlet pair tunneling is enhanced and magnetic correlations are strongly reduced. This suggests a possible superconductive ground state.

cond-mat.str-el↗
arXiv2006

Critical Exponents in a Quantum Phase Transition of an Anisotropic 2D Antiferromagnet

I use the two-step density-matrix renormalization group method to extract the critical exponents $β$ and $ν$ in the transition from a Néel $Q=(π,π)$ phase to a magnetically disordered phase with a spin gap. I find that the exponent $β$ computed from the magnetic side of the transition is consistent with that of the classical Heisenberg model, but not the exponent $zν$ computed from the disordered side. I also show the contrast between integer and half-integer spin cases.

cond-mat.str-el↗
arXiv2005

Néel and disordered phases of coupled Heisenberg chains with $S=1/2$ to S=4

We use the two-step density-matrix renormalization group method to study the effects of frustration in Heisenberg models for $S=1/2$ to S=4 in a two-dimensional anisotropic lattice. We find that as in $S=1/2$ studied previously, the system is made of nearly disconnected chains at the maximally frustrated point, $J_d/J_{\perp}=0.5$, i.e., the transverse spin-spin correlations decay exponentially. This leads to the following consequences: (i) all half-integer spins systems are gapless, behaving like a sliding Luttinger liquid as in $S=1/2$; (ii) for integer spins, there is an intermediate disordered phase with a spin gap, with the width of the disordered state is roughly proportional to the 1D Haldane gap.

cond-mat.str-el↗
arXiv2005

Quantum phase transition and sliding Luttinger liquid in coupled t-J chains

Using a recently proposed perturbative numerical renormalization-group algorithm, we explore the connection between quantum criticality and the emergence of Luttinger liquid physics in $t-J$ chains coupled by frustrated interactions. This study is built on an earlier finding that at the maximally frustrated point, the ground state of weakly-coupled Heisenberg chains is disordered, the transverse exchanges being irrelevant. This result is extended here to transverse couplings up to $J_{\perp}=0.6$, and we argue that it may also be valid at the isotropic point. A finite size analysis of coupled Heisenberg chains in the vicinity of the maximally frustrated point confirms that the transverse spin-spin correlations decay exponentially while the longitudinal ones revert to those of decoupled chains. We find that this behavior persists upon moderate hole doping $x \alt 0.75$. For larger doping, the frustration becomes inactive and the quantum critical point is suppressed.

cond-mat.str-el↗
arXiv2004

Renormalization group method for weakly-coupled quantum chains: application to the spin one-half Heisenberg model

The Kato-Bloch perturbation formalism is used to present a density-matrix renormalization-group (DMRG) method for strongly anisotropic two-dimensional systems. This method is used to study Heisenberg chains weakly coupled by the transverse couplings $J_{\perp}$ and $J_{d}$ (along the diagonals). An extensive comparison of the renormalization group and quantum Monte Carlo results for parameters where the simulations by the latter method are possible shows a very good agreement between the two methods. It is found, by analyzing ground state energies and spin-spin correlation functions, that there is a transition between two ordered magnetic states. When $J_{d}/J_{\perp} \alt 0.5$, the ground state displays a Néel order. When $J_{d}/J_{\perp} \agt 0.5$, a collinear magnetic ground state in which interchain spin correlations are ferromagnetic becomes stable. In the vicinity of the transition point, $J_{d}/J_{\perp} \approx 0.5$, the ground state is disordered. But, the nature of this disordered ground state is unclear. While the numerical data seem to show that the chains are disconnected, the possibility of a genuine disordered two-dimensional state, hidden by finite size effects, cannot be excluded.

cond-mat.str-el↗
arXiv2004

Disordered and Ordered States in a Frustrated Anisotropic Heisenberg Hamiltonian

We use a recently proposed perturbative numerical renormalization group algorithm to investigate ground-state properties of a frustrated three dimensional Heisenberg model on an anisotropic lattice. We analyze the ground state energy, the finite size spin gap and the static magnetic structure factor. We find in two dimensions a frustration-induced gapless spin liquid state which separates two magnetically ordered phases. In the spin liquid state, the magnetic structure factor shows evidence that this state is made of nearly disconnected chains. This spin liquid state is unstable against unfrustrated interplane couplings.

cond-mat.str-el↗
arXiv2004

Renormalization group method for weakly coupled quantum chains: comparison with exact diagonalization

We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg spin ladders with a transverse Hamiltonian that can involve frustration. Due to the variational nature of the algorithm, the accuracy can be arbitrarily improved enlarging the basis of eigenstates of the density matrix defined in the transverse direction. We observe that the precision of the algorithm is directly correlated to the binding of the chains. We also show that the method performs especially well in frustrated systems.

cond-mat.str-el↗
arXiv2003

A Matrix Kato-Bloch Perturbation Method for Hamiltonian Systems

A generalized version of the Kato-Bloch perturbation expansion is presented. It consists of replacing simple numbers appearing in the perturbative series by matrices. This leads to the fact that the dependence of the eigenvalues of the perturbed system on the strength of the perturbation is not necessarily polynomial. The efficiency of the matrix expansion is illustrated in three cases: the Mathieu equation, the anharmonic oscillator and weakly coupled Heisenberg chains. It is shown that the matrix expansion converges for a suitably chosen subspace and, for weakly coupled Heisenberg chains, it can lead to an ordered state starting from a disordered single chain. This test is usually failed by conventional perturbative approaches.

physics.comp-ph↗
arXiv2003

A Renormalization Group Method for Quasi One-dimensional Quantum Hamiltonians

A density-matrix renormalization group (DMRG) method for highly anisotropic two-dimensional systems is presented. The method consists in applying the usual DMRG in two steps. In the first step, a pure one dimensional calculation along the longitudinal direction is made in order to generate a low energy Hamiltonian. In the second step, the anisotropic 2D lattice is obtained by coupling in the transverse direction the 1D Hamiltonians. The method is applied to the anisotropic quantum spin half Heisenberg model on a square lattice.

cond-mat.str-el↗
arXiv2001

A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation

We present the algorithmic details of the dynamical cluster approximation (DCA), with a quantum Monte Carlo (QMC) method used to solve the effective cluster problem. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA) while preserving the lattice symmetries. The DCA becomes exact for an infinite cluster size, while reducing to the DMFA for a cluster size of unity. We present a generalization of the Hirsch-Fye QMC algorithm for the solution of the embedded cluster problem. We use the two-dimensional Hubbard model to illustrate the performance of the DCA technique. At half-filling, we show that the DCA drives the spurious finite-temperature antiferromagnetic transition found in the DMFA slowly towards zero temperature as the cluster size increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that there is a finite temperature metal to insulator transition which persists into the weak-coupling regime. This suggests that the magnetism of the model is Heisenberg like for all non-zero interactions. Away from half-filling, we find that the sign problem that arises in QMC simulations is significantly less severe in the context of DCA. Hence, we were able to obtain good statistics for small clusters. For these clusters, the DCA results show evidence of non-Fermi liquid behavior and superconductivity near half-filling.

cond-mat.str-el↗