arXiv subjects
Publications and source records attributed to F. F. Assaad.
In our reply, we show that the objections put forward in cond-mat/0508763 concerning our paper, Phys. Rev. Lett. 93, 136405 (2004), are not valid: (i) There is no orthogonality catastrophe (OC) for our calculations, and it is also generally not ``unpractical'' to avoid it. (ii) The OC does not affect our results.
Katsnelson submitted his Comment on our paper "Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory" to Phys. Rev. Lett. in May 2005. We proved in our report that this comment was incorrect since there is no orthogonality catastrophe for our calculation in Phys. Rev. Lett. 93, 136405 (2004) which is for half-filling. Now in cond-mat/0508763, Katsnelson incorporates our proof of the invalidity of his original Comment, based on Friedel's sum rule. Instead, he now claims that the projective quantum Monte Carlo method is "unpractical" off half-filling, overlooking that our calculations off half-filling (R. Arita and K. Held, LT24 conference proceedings and cond-mat/0508639) employ in practice a noninteracting trial Hamiltonian with the same electron density as the interacting Hamiltonian so that there is again no orthogonality catastrophe. Note added. In the revised version of his comment, Katsnelson gives proper credit to our proof. In our reply, we will present the original proof based on the Friedel sum rule. Moreover, we show that the orthogonality catastrophe does not affect our results. Katsnelson's objection is not valid.
We study the temperature dependence of the single particle spectral function as well as of the dynamical spin and charge structure factors for the one-dimensional Hubbard model using the finite temperature auxiliary field quantum Monte Carlo algorithm. The parameters of our simulations are chosen so to at best describe the low temperature photoemission spectra of the organic conductor TTF-TCNQ. Defining a magnetic energy scale, T_J, which marks the onset of short ranged 2k_f magnetic fluctuations, we conclude that for temperatures T < T_J the ground state features of the single particle spectral function are apparent in the finite temperature data. Above T_J spectral weight transfer over a scale set by the hopping t is observed. In contrast, photoemission data points to a lower energy scale below which spectral weight transfer occurs. Discrepancies between Hubbard model calculations and experiments are discussed.
A novel sign-free Monte Carlo method for the Hubbard model has recently been proposed by Corney and Drummond. High precision measurements on small clusters show that ground state correlation functions are not correctly reproduced. We argue that the origin of this mismatch lies in the fact that the low temperature density matrix does not have the symmetries of the Hamiltonian. Here we show that supplementing the algorithm with symmetry projection schemes provides reliable and accurate estimates of ground state properties.
We study the dynamic response of ultracold bosons trapped in one-dimensional optical lattices using Quantum Monte Carlo simulations of the boson Hubbard model with a confining potential. The dynamic structure factor reveals the inhomogeneous nature of the low temperature state, which contains coexisting Mott insulator and superfluid regions. We present new evidence for local quantum criticality and shed new light on the experimental excitation spectrum of 87Rb atoms confined in one dimension.
We investigate the phase diagram of the half-filled SU(N) Hubbard-Heisenberg model with hopping t, exchange J and Hubbard U, on a square lattice. In the large-N limit, and as a function of decreasing values of t/J, the model shows a transition from a d-density wave state to a spin dimerized insulator. A similar behavior is observed at N=6 whereas at N=2 a spin density wave insulating ground state is stabilized. The N=4 model, has a d-density wave ground state at large values of t/J which as a function of decreasing values of t/J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power-law,resulting in gapless spin excitations at q = (pi,pi). Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors q = (0,pi) and q = (pi,0). This gapless spin liquid state is equally found in the SU(4) Heisenberg model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a pi-flux phase is offered. Our results stem from projective (T=0) quantum Monte-Carlo simulations on lattice sizes ranging up to 24 X 24.
We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the one-band Hubbard model, reconfirming the numerical renormalization group results.
A doped hole in the two-dimensional half-filled Kondo lattice model with exchange J and hopping t has momentum (pi,pi) irrespective of the coupling J/t. The quasiparticle residue of the doped hole, Z_{(π, π)}, tracks the Kondo scale, T_K, of the corresponding single impurity model. Those results stem from high precision quantum Monte Carlo simulations on lattices up to 12 X 12. Accounting for small dopings away from half-filling within a rigid band approximation, this result implies that the effective mass of the charge carriers at the Fermi level tracks 1/T_K or equivalently that the coherence temperature T_{coh} \propto T_K. This results is consistent with the large-N saddle point of the SU(N) symmetric Kondo lattice model.
We study the 2D Kondo insulators in a uniform magnetic field using quantum Monte Carlo simulations of the particle-hole symmetric Kondo lattice model and a mean field analysis of the Periodic Anderson model. We find that the field induces a transition to an insulating, antiferromagnetically ordered phase with staggered moment in the plane perpendicular to the field. For fields in excess of the quasi-particle gap, corresponding to a metal in a simple band picture of the periodic Anderson model, we find that the metallic phase is unstable towards the spin density wave type ordering for any finite value of the interaction strength. This can be understood as a consequence of the perfect nesting of the particle and hole Fermi surfaces that emerge as the field closes the gap. We propose a phase diagram and investigate the quasi-particle and charge excitations in the magnetic field. We find good agreement between the mean-field and quantum Monte Carlo results.
Using a newly developed hybrid Monte Carlo algorithm for the nearest-neighbor (n.n.) t-J model, we show that antiholons identified in the supersymmetric inverse squared (IS) t-J model are clearly visible in the electron addition spectrum of the n.n. t-J model at J=2t and also for J=0.5t, a value of experimental relevance.
We study the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector Quantum Monte Carlo method. Upon varying the Hubbard $U$ from attractive to repulsive we find a first order phase transition between superconducting and antiferromagnetic states.
We study spin and charge dynamics of stripes in doped Mott insulators by considering a two-dimensional Hubbard model with N fermion flavors. For N =2 we recover the normal one-band model while for N -> infty a spin density wave mean-field solution. For all band fillings, lattice topologies and N= 4 n the model may be solved by means of Monte Carlo methods without encountering the sign problem. At N=4 and in the vicinity of the Mott insulator, the single particle density of states shows a gap. Within this gap and on rectangular topologies of sizes up to 30 X 12 we find gapless spin collective modes centered around q = (π\pm ε_x,π\pm ε_y) as well as charge modes centered around q = (\pm 2 ε_x, \pm 2 ε_y), q = (\pm ε_x, \pm ε_y) and q = (0,0). ε_{x,y} depends on the lattice topology and doping.
We consider a two dimensional Kondo lattice model with exchange J and hopping t in which three out of four impurity spins are removed in a regular way. At the particle-hole symmetric point the model may be studied with auxiliary field quantum Monte Carlo methods without sign problems. To achieve the relevant energy scales on finite clusters, we introduce a simple method to reduce size effects by up to an order of magnitude in temperature. In this model, a metallic phase survives up to arbitrarily low temperatures before being disrupted by magnetic fluctuations which open a gap in the charge sector. We study the formation of the heavy-electron state with emphasis on a crossover scale T* defined by the maximum in the resistivity versus temperature curve. The behavior of thermodynamic properties such as specific heat as well as spin and charge uniform susceptibilities are studied as the temperature varies in a wide range across T*. Within our accuracy T* compares well to the Kondo scale of the related single impurity problem. Finally our QMC resuls are compared with mean-field approximations.
We consider the Kondo lattice model in two dimensions at half filling. In addition to the fermionic hopping integral $t$ and the superexchange coupling $J$ the role of a Coulomb repulsion $U$ in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of J_c which is decreasing as a function of U. The single particle spectral function A(k,w) is computed across this transition. For all values of J > 0, and apart from shadow features present in the ordered state, A(k,w) remains insensitive to the magnetic phase transition with the first low-energy hole states residing at momenta k = (\pm π, \pm π). As J -> 0 the model maps onto the Hubbard Hamiltonian. Only in this limit, the low-energy spectral weight at k = (\pm π, \pm π) vanishes with first electron removal-states emerging at wave vectors on the magnetic Brillouin zone boundary. Thus, we conclude that (i) the local screening of impurity spins determines the low energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the Mott-Hubbard insulator at J=0 to that of the Kondo insulator at J > J_c. Our results are based on both, T=0 Quantum Monte-Carlo simulations and a bond-operator mean-field theory.
Optical reflection measurements within the highly conducting (a,b)-plane of the organic metal (BEDT-TTF)_4[Ni(dto)_2] reveal the gradual development of a sharp feature at around 200 cm as the temperature is reduced below 150 K. Below this frequency a narrow Drude-like response is observed which accounts for the metallic behavior. Since de Haas-von Alphen oscillations at low temperatures confirm band structure calculations of bands crossing the Fermi energy, we assign the observed behavior to a two-dimensional metallic state in the proximity of a correlation induced metal-insulator transition.
We present a detailed numerical study of spin and charge dynamics of the two-dimensional Kondo lattice model with hopping t and exchange J. At T=0 and J > 0, the competition between the RKKY interaction and Kondo effect triggers a quantum phase transition between magnetically ordered and disordered insulators: J_c/t = 1.45(5). The quasiparticle gap scales as |J|. S(q,ω), evolves smoothly from its strong coupling form with spin gap at q = (π,π) to a spin wave form. At J>0, A(\vec{k},ω) shows a dispersion relation following that of hybridized bands. For J < J_c this feature is supplemented by shadows thus pointing to a coexistence of Kondo screening and magnetism. For J < 0 A(\vec{k},ω) is similar to that of non-interacting electrons in a staggered magnetic field. Spin, T_S, and charge, T_C, scales are defined. For weak to intermediate couplings, T_S marks the onset of antiferromagnetic fluctuations and follows a J^2 law. At strong couplings T_S scales as J. T_C scales as J both at weak and strong couplings. At and slightly below T_C we observe i) a rise in the resistivity as a function of decreasing temperature, ii) a dip in the integrated density of states at the Fermi energy and iii) the occurrence of hybridized bands in A(k,ω). It is shown that in the weak coupling limit, the charge gap of order J is of magnetic origin. The specific heat shows a two peak structure, the low temperature peak being of magnetic origin. Our results are compared to various mean-field theories.
The calculation of imaginary time displaced correlation functions with the auxiliary field projector quantum Monte-Carlo algorithm provides valuable insight (such as spin and charge gaps) in the model under consideration. One of the authors and M. Imada [F.F. Assaad and M. Imada, J. Phys. Soc. Jpn. 65 189 (1996).] have proposed a numerically stable method to compute those quantities. Although precise this method is expensive in CPU time. Here, we present an alternative approach which is an order of magnitude quicker, just as precise, and very simple to implement. The method is based on the observation that for a given auxiliary field the equal time Green function matrix, $G$, is a projector: $G^2 = G$.
The 2D half-filled Kondo lattice model with exchange J and nearest neighbor hopping t is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment, spin and quasiparticle gaps on lattice sizes up to 12 X 12. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gaped insulators. This transition occurs at J/t = 1.45 \pm 0.05.