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G. George Batrouni

Publications and source records attributed to G. George Batrouni.

At least 19 recordsLinked to original sources
arXiv2025

Disorder and the Robustness of Superconductivity on the Flat Band

We study the interplay between on-site disorder and fermion pairing on the quasi one-dimensional flat band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat band superconductivity is robust against disorder: The critical disorder strength, $W_c$, required to localize the fermion pairs and destroy superconductivity, is finite at any interaction strength, $U$, and is proportional to the superconducting weight, $D_s$, of the clean system. Using large scale density matrix renormalization group computations, we show that this transition is of the BKT form. In addition, even at very small interaction strength, the localization is not due to single fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that $W_c$ can be accurately determined by using an appropriate scaling function.

cond-mat.supr-con↗
arXiv2023

Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling

The Su-Schrieffer-Heeger (SSH) model, with bond phonons modulating electron tunneling, is a paradigmatic electron-phonon model that hosts an antiferromagnetic order to bond order transition at half-filling. In the presence of repulsive Hubbard interaction, the antiferromagnetic phase is enhanced, but the phase transition remains first-order. Here we explore the physics of the SSH model with attractive Hubbard interaction, which hosts an interesting interplay among charge order, s-wave pairing, and bond order. Using the numerically exact determinant quantum Monte Carlo method, we show that both charge order, present at weak electron-phonon coupling, and bond order, at large coupling, give way to s-wave pairing when the system is doped. Furthermore, we demonstrate that the SSH electron-phonon interaction competes with the attractive Hubbard interaction and reduces the s-wave pairing correlation.

cond-mat.str-el↗
arXiv2023

Superconductivity with Wannier-Stark Flat Bands

We investigate superconducting transport in the DC field induced Wannier-Stark flat bands in the presence of interactions. Flat bands offer the possibility of unconventional high temperature superconductivity, where the superfluid weight, $D_s$, is enhanced by the density overlap of the localized states. However, construction of flat bands typically requires very precise tuning of Hamiltonian parameters. To overcome this difficulty, we propose a feasible alternative to realize flat bands by applying a DC field in a commensurate lattice direction. We systematically characterize the superconducting behavior on these flat bands by studying the effect of the DC field and attractive Hubbard interaction strengths on the wavefunction, correlation length, pairing order parameter and the superfluid weight $D_s$. Our main result is that the superfluid weight is dramatically enhanced at an optimal value of the interaction strength and weak DC fields.

cond-mat.supr-con↗
arXiv2018

Pairing and superconductivity in the flat band: Creutz lattice

We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely the Creutz lattice, where we investigate the role of local attractive interactions in the $U < 0$ Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.

cond-mat.str-el↗
arXiv2017

Interaction-Induced Gradients Across a Confined Fermion Lattice

An imposed chemical potential gradient $A_\uparrow=dμ_\uparrow/dx$ on a single fermionic species ("spin up") directly produces a gradient in the density $dρ_\uparrow/dx$ across a lattice. We study here the induced density inhomogeneity $dρ_\downarrow/dx$ in the second fermionic species ("spin down") which results from fermionic interactions $U$, even in the absence of a chemical potential gradient $A_\downarrow=0$ on that species. The magnitude of $dρ_\downarrow/dx$ acquired by the second species grows with $U$, while the magnitude of $dρ_\uparrow/dx$ remains relatively constant, that is, set only by $A_\uparrow$. For a given $A_\uparrow$, we find an interaction strength $U_*$ above which the two density gradients are equal in magnitude. We also evaluate the spin-spin correlations and show that, as expected, antiferromagnetism is most dominant at locations where the local density is half-filled. The spin polarization induced by sufficiently large gradients, in combination with $U$, drives ferromagnetic behavior. In the case of repulsive interactions, $dρ_\downarrow/dx = -dρ_\uparrow/dx$. A simple particle-hole transformation determines the related effect in the case of attractive interactions.

cond-mat.quant-gas↗
arXiv2016

Haldane phase in the sawtooth lattice: Edge states, entanglement spectrum and the flat band

Using density matrix renormalization group numerical calculations, we study the phase diagram of the half filled Bose-Hubbard system in the sawtooth lattice with strong frustration in the kinetic energy term. We focus in particular on values of the hopping terms which produce a flat band and show that, in the presence of contact and near neighbor repulsion, three phases exist: Mott insulator (MI), charge density wave (CDW), and the topological Haldane insulating (HI) phase which displays edge states and particle imbalance between the two ends of the system. We find that, even though the entanglement spectrum in the Haldane phase is not doubly degenerate, it is in excellent agreement with the entanglement spectrum of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state built in the Wannier basis associated with the flat band. This emphasizes that the absence of degeneracy in the entanglement spectrum is not necessarily a signature of a non-topological phase, but rather that the (hidden) protecting symmetry involves non-local states. Finally, we also show that the HI phase is stable against small departure from flatness of the band but is destroyed for larger ones.

cond-mat.quant-gas↗
arXiv2006

Self-Affinity in the Gradient Percolation Problem

We study the scaling properties of the solid-on-solid front of the infinite cluster in two-dimensional gradient percolation. We show that such an object is self affine with a Hurst exponent equal to 2/3 up to a cutoff-length proportional to the gradient to the power (-4/7). Beyond this length scale, the front position has the character of uncorrelated noise. Importantly, the self-affine behavior is robust even after removing local jumps of the front. The previously observed multi affinity, is due to the dominance of overhangs at small distances in the structure function. This is a crossover effect.

cond-mat.dis-nn↗
arXiv2006

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

We report results of quantum Monte Carlo simulations in the canonical and the grand-canonical ensemble of the two- and three-dimensional Bose-Hubbard model with quadratic and quartic confining potentials. The quantum criticality of the superfluid-Mott insulator transition is investigated both on the boundary layer separating the two coexisting phases and at the center of the traps where the Mott-insulating phase is first established. Recent simulations of systems in quadratic traps have shown that the transition is not in the critical regime due to the finite gradient of the confining potential and that critical fluctuations are suppressed. In addition, it has been shown that quantum critical behavior is recovered in flat confining potentials as they approach the uniform regime. Our results show that quartic traps display a behavior similar to quadratic ones, yet locally at the center of the traps the bulk transition has enhanced critical fluctuations in comparison to the quadratic case. Therefore quartic traps provide a better prerequisite for the experimental observation of true quantum criticality of ultracold bosonic atoms in optical lattices.

cond-mat.other↗
arXiv2006

Bragg spectroscopy of trapped one dimensional strongly interacting bosons in optical lattices: Probing the cake-structure

We study Bragg spectroscopy of strongly interacting one dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard Hamiltonian, exact diagonalizations and the results of a recently introduced effective fermionization (EF) model. We find that, due to the system's inhomogeneity, the excitation spectrum exhibits a multi-branched structure, whose origin is related to the presence of superfluid regions with different densities in the atomic distribution. We thus suggest that Bragg spectroscopy in the linear regime can be used as an experimental tool to unveil the shell structure of alternating Mott insulator and superfluid phases characteristic of trapped bosons.

cond-mat.other↗
arXiv2004

Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas

We present results from quantum Monte Carlo simulations of trapped bosons in optical lattices, focusing on the crossover from a gas of softcore bosons to a Tonks-Girardeau gas in a one-dimensional optical lattice. We find that depending on the quantity being measured, the behavior found in the Tonks-Girardeau regime is observed already at relatively small values of the interaction strength. A finite critical value for entering the Tonks-Girardeau regime does not exist. Furthermore, we discuss the computational efficiency of two quantum Monte Carlo methods to simulate large scale trapped bosonic systems: directed loops in stochastic series expansions and the worm algorithm.

cond-mat.stat-mech↗
arXiv2004

Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices

We study properties of ultra-cold bosonic atoms in one, two and three dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose Hubbard model in parabolic confinement potentials. Local phase structures of the atoms are shown to be accessible via a well defined local compressibility, quantifying a global response of the system to a local perturbation. An indicator for the presence of extended Mott plateaux is shown to stem from the shape of the coherent component of the momentum distribution function, amenable to experimental detection. Additional fine structures in the momentum distribution are found to appear unrelated to the local phase structure, disproving previous claims. We discuss limitations of local potential approximations for confined Bose gases, and the absence of quantum criticality and critical slowing down in parabolic confinement potentials, thus accounting for the fast dynamics in establishing phase coherence in current experiments. In contrast, we find that flat confinement potentials allow quantum critical behavior to be observed already on moderately sized optical lattices. Our results furthermore demonstrate, that the experimental detection of the Mott transition would be significantly eased in flat confinement potentials.

cond-mat.stat-mech↗
arXiv2002

Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone

We show that the roughness exponent zeta of an in-plane crack front slowly propagating along a heterogeneous interface embeded in a elastic body, is in full agreement with a correlated percolation problem in a linear gradient. We obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We develop an elastic brittle model based on both the 3D Green function in an elastic half-space and a discrete interface of brittle fibers and find numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We also obtain by direct numerical simulations zeta=0.6 in excellent agreement with our prediction. This modelling is for the first time in close agreement with experimental observations.

cond-mat↗
arXiv2001

Heterogeneous Interfacial Failure between Two Elastic Blocks

We investigate numerically the failure process when two elastic media, one hard and one soft that have been glued together thus forming a common interface, are pulled apart. We present three main results: (1) The area distribution of simultaneously failing glue (bursts) follows a power law consistent with the theoretically expected exponent 2.5, (2) the maximum load and displacement before catastrophic failure scale as L^2 and L^0 respectively, where L is the linear size of the system, and (3) the area distribution of failed glue regions (clusters) is a power law with exponent -1.6 when the system fails catstrophically.

cond-mat↗
arXiv2000

Elastic Response of Rough Surfaces in Partial Contact

We model numerically the partial normal contact of two elastic rough surfaces with highly correlated asperities. Facing surfaces are unmated and described as self-affine with a Hurst exponent H. The numerical algorithm is based on Fourier acceleration and allows efficient simulation of very large systems. The force, F, versus contact area, A, characteristics follows the law F = c A^[(1+H)/2] in accordance with the suggestion of Roux et al. (Europhys. Lett. 23, 277 (1993)). However finite size corrections are very large even for 512X512 systems where the effective exponent is still 20% larger than its asymptotic value.

cond-mat↗
arXiv2000

Normal Stress Distribution of Rough Surfaces in Contact

We study numerically the stress distribution on the interface between two thick elastic media bounded by interfaces that include spatially correlated asperities. The interface roughness is described using the self-affine topography that is observed over a very wide range of scales from fractures to faults. We analyse the correlation properties of the normal stress distribution when the rough surfaces have been brought into full contact. The self affinity of the rough surfaces is described by a Hurst exponent H. We find that the normal stress field is also self affine, but with a Hurst exponent H-1. Fluctations of the normal stress are shown to be important, especially at local scales with anti-persistent correlations.

cond-mat↗
arXiv1997

Fracture in Three-Dimensional Fuse Networks

We report on large scale numerical simulations of fracture surfaces using random fuse networks for two very different disorders. There are some properties and exponents that are different for the two distributions, but others, notably the roughness exponents, seem universal. For the universal roughness exponent we found a value of zeta = 0.62 +/- 0.05. In contrast to what is observed in two dimensions, this value is lower than that reported in experimental studies of brittle fractures, and rules out the minimal energy surface exponent, 0.41 +/- 0.01.

cond-mat.soft↗
arXiv1997

A two-dimensional network simulator for two-phase flow in porous media

We investigate a two-dimensional network simulator capable of modeling different time dependencies in two-phase drainage displacements. In particular, we focus on the temporal evolution of the pressure due to capillary and viscous forces and the time dependence of the interface between the two liquids. The dynamics of the capillary effect are taken into account and we report on high accuracy pressure measurements. Moreover, the simulator includes important features in drainage, like burst dynamics of the invading fluid and simultaneous flow of two liquids in a section of a tube. The validity of the model is checked by comparing simulation results with well known experimental properties in drainage displacement.

physics.flu-dyn↗