Reply to a Comment on ``Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory''

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.Comment: 1 page, 1 figure, Phys. Rev. Lett. in print; also note cond-mat/050944

Comment on "Quantum Monte Carlo Evidence for Superconductivity in the Three-Band Hubbard Model in Two Dimensions"

In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.Comment: 1 page latex and 2 eps-figures, uses epsfig, submitted to PR

Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices

We present an exact study of the finite-temperature properties of hard-core bosons (HCB's) confined on one-dimensional optical lattices. Our solution of the HCB problem is based on the Jordan-Wigner transformation and properties of Slater determinants. We analyze the effects of the temperature on the behavior of the one-particle correlations, the momentum distribution function, and the lowest natural orbitals. In addition, we compare results obtained using the grand-canonical and canonical descriptions for systems like the ones recently achieved experimentally. We show that even for such small systems, as small as 10 HCB's in 50 lattice sites, there are only minor differences between the energies and momentum distributions obtained within both ensembles.Comment: RevTex file, 12 pages, 16 figures, published versio

Critical Exponents of the Metal-Insulator Transition in the Two-Dimensional Hubbard Model

We study the filling-controlled metal-insulator transition in the two-dimensional Hubbard model near half-filling with the use of zero temperature quantum Monte Carlo methods. In the metallic phase, the compressibility behaves as $\kappa \propto |\mu - \mu_c|^{-0.58\pm0.08}$ where $\mu_c$ is the critical chemical potential. In the insulating phase, the localization length follows $\xi_l \propto |\mu - \mu_c|^{-\nu_l}$ with $\nu_l = 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent $\nu_\kappa = 0.21 \pm 0.04$. Our results show that the exponents $\nu_\kappa$ and $\nu_l$ agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast the metal-insulator transition in the generic band insulators in all dimensions as well as in the one-dimensional Hubbard model satisfy the hyperscaling assumption with exponents $\nu = 1/2$ and $z = 2$.Comment: Two references added. The DVI file and PS figure files are also available at http://www.issp.u-tokyo.ac.jp/labs/riron/imada/furukawa/; to appear in J. Phys. Soc. Jpn 65 (1996) No.

Dynamic Exponent of t-J and t-J-W Model

Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, $W$. For the ordinary t-J model with $W$=0, the scaling of the Drude weight $D \propto \delta^2$ for small doping concentration $\delta$ is obtained, which indicates anomalous dynamic exponent $z$=4 of the Mott transition. When $W$ is switched on, the dynamic exponent recovers its conventional value $z$=2. This corresponds to an incoherent-to-coherent transition associated with the switching of the two-particle transfer.Comment: LaTeX, JPSJ-style, 4 pages, 5 eps files, to appear in J. Phys. Soc. Jpn. vol.67, No.6 (1998

Identifiability of direct effects from summary causal graphs

Dynamic structural causal models (SCMs) are a powerful framework for reasoning in dynamic systems about direct effects which measure how a change in one variable affects another variable while holding all other variables constant. The causal relations in a dynamic structural causal model can be qualitatively represented with a full-time causal graph. Assuming linearity and causal sufficiency and given the full-time causal graph, the direct causal effect is always identifiable and can be estimated from data by adjusting on any set of variables given by the so-called single-door criterion. However, in many application such a graph is not available for various reasons but nevertheless experts have access to an abstraction of the full-time causal graph which represents causal relations between time series while omitting temporal information. This paper presents a complete identifiability result which characterizes all cases for which the direct effect is graphically identifiable from summary causal graphs and gives two sound finite adjustment sets that can be used to estimate the direct effect whenever it is identifiable

Doping induced metal-insulator transition in two-dimensional Hubbard, t−Ut-U, and extended Hubbard, t−U−Wt-U-W, models

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2}$ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor.Comment: 19 pages (latex) including 7 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.