Section 1 Introduction

We present quantum Monte Carlo results for the Hubbard model on a ladder using the restructuring method which employ eigenstates of two-site system on a rung to construct a complete set. From technical reasons we concentrate on the case in which the hopping along the leg is much less than the hopping on the rung. We observe the ground state of the half-filled system is made of singlet-like states described in this paper and its first excited state contains one triplet rung. When the system is lightly doped states composed of an electron and a hole appear on some rungs. We find very few hole-pairing on the rung upon doping up to the quarter-filled case. Lately strongly correlated systems of electrons on ladders with two or more legs have become quite intriguing from both theoretical and experimental points of view. Various models are numerically investigated by means of exact diagonaliza-tion [1, 2, 3] and renormalization group approaches [4, 5, 6]. Active studies on the quantum spin ladder systems, which correspond to the half-filled fermionic ladders with infinite Coulomb repulsion, are also stimulative [7]. Among their results, especially interesting are spin gaps, ground states as well as excited states of the systems and formation of the hole-pair bound state. Presence of spin gaps is reported for several spin systems and for fermion systems such as the t-J-t ′-J ′ model on a single ladder (two coupled chains) studied in Ref. [1], the t-J model on a single ladder [2] and on multi-ladders with even number of coupled chains [3], and the two-chain Hubbard Model [4]. In Refs. [1, 2] emergence of the hole-pairing upon doping, which would indicate the high T c superconductivity, is also claimed. Quantum Monte Carlo techniques based on the Suzuki-Trotter formula, which prove useful for many spin systems [8, 9], are difficult to apply to the fermion systems because of the negative sign problem except for those on a single chain [10]. Usually studies on the two-dimensional fermion systems have been done after integrating the fermionic degrees of freedom [11, 12, 13, 14]. Yet it would be desirable to simulate such electron systems keeping fermionic degrees of freedom and vividly observe how electrons and holes behave on ladders. Recently dynamical properties of the half-filled Hubbard ladder are studied by Scalapino et al. [6] using grand canonical quantum Monte Carlo calculations with maximum entropy analytic continuation. In this …