As well known, the surface Andreev bound state (ABS) forms at the open (1, 1) edge of a d x 2 −y 2wave superconductor. Although large local density of states (LDOS) in the ABS can lead to the emergence of exotic strongly correrated electronic states, theoretical studies on this issue has been limited. To understand important effects of ABS on the electronic correlation, we study the cluster Hubbard model with an open (1, 1) edge in the presence of a bulk d-wave gap. We calculate the site-dependent spin susceptibility by performing random phase approximation (RPA) and fluctuation exchange (FLEX) approximation in the real space. We find that at the (1, 1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk d-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.

Amebic liver abscesses (ALAs) are the most commonly encountered extraintestinal manifestation of human invasive amebiasis, which results from Entamoeba histolytica ( E. histolytica ) spreading extraintestinally. Amebiasis can be complicated by liver abscess in 9% of cases, and ALAs led to almost 50000 fatalities worldwide in 2010. Although there have been fewer and fewer cases in the past several years, ALAs remain an important public health problem in endemic areas. E. histolytica causes both amebic colitis and liver abscess by breaching the host’s innate defenses and invading the intestinal mucosa. Trophozoites often enter the circulatory system, where they are filtered in the liver and produce abscesses, and develop into severe invasive diseases such as ALAs. The clinical presentation can appear to be colitis, including upper-right abdominal pain accompanied by a fever in ALA cases. Proper diagnosis requires nonspecific liver imaging as well as detecting anti- E. histolytica antibodies; however, these antibodies cannot be used to distinguish between a previous infection and an acute infection. Therefore, diagnostics primarily aim to use PCR or enzyme-linked immunosorbent assay to detect E. histolytica . ALAs can be treated medically, and percutaneous catheter drainage is only necessary in approximately 15% of cases. The indicated treatment is to administer an amebicidal drug (such as tinidazole or metronidazole) and paromomycin or other luminal cysticidal agent for clinical disease. Prognosis is good with almost universal recovery. Establishing which diagnostic methods are most efficacious will necessitate further analysis of similar clinical cases.

To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The positiondependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order.In strongly correlated electron systems, many-body electronic states are drastically modified by introducing real-space structures, such as the defects and domain boundaries. To predict exotic electronic properties created by introducing the defects in real space, it is important to develop theoretical methods of analyzing the strongly correlated metals without translational symmetry. In cuprate high-T c superconductors, for example, single nonmagnetic impurity on Cu-site induces the local moment with ∼ 1µ B in both YBa 2 Cu 3 O 7−x (YBCO) [1] and La 2−δ Sr δ CuO 4 (LSCO) [2]. It was revealed by the NMR study [3][4][5] that both the local and the staggered spin susceptibilities are strongly enhanced around the impurity site. In addition, dilute nonmagnetic impurities cause huge residual resistivity beyond the s-wave unitary scattering limit in cuprate superconductors [6] and heavy-fermion systems [7,8]. Thus, the system approaches to the magnetic quantum-critical point (QCP) by introducing dilute point defects. [9].

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