We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks Z4 symmetry, as recently seen in the hidden order phase of URu2Si2. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.

We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group ͑RG͒ approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight Z along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.

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Hospital das Clínicas da UFPE. Doutor e Livre-Docente pela UFPE. Fellow do American College of Surgeons (FACS) e do Surgical Infection Society.Recebido em 1/12/99 Aceito para publicação em 25/7/2000 Trabalho apresentado no XXIII Congresso Brasileiro de Cirurgia -Rio de Janeiro -1999. RESUMO:Objetivo: A hipertensão portal esquistossomótica com antecedente de hemorragia digestiva foi tratada com esplenectomia + ligadura da veia gástrica esquerda (LVGE) + desvascularização da grande curvatura do estômago + esclerose endoscópica pós-operatória. Quando da existência de varizes de fundo gástrico, realizamos a abertura do fundo gástrico e sutura obliterante destas varizes. O objetivo deste trabalho foi avaliar a recidiva de hemorragia digestiva, repercussões laboratoriais e mortalidade do tratamento cirúrgico/endoscó-pico. Métodos: Entre 1992 e 1998, foram operados no HC-UFPE 131 pacientes. O seguimento médio foi de 30 meses, em 111 pacientes, que foram solicitados a retornar ao ambulatório do HC-UFPE para a realização de controle clínico e laboratorial. Resultados: A recidiva hemorrágica foi de 14,4% (16/111) e uma mortalidade de 5,4% (6/111). A recidiva de hemorragia digestiva alta foi exteriorizada através de hematemese em oito pacientes e oito por melena. Dos seis pacientes que foram a óbito, três apresentavam diagnóstico de linfoma, hepatocarcinoma e infarto agudo do miocárdio, respectivamente. Dois pacientes foram a óbito no pós-operatório imediato (sepse e coagulação intravascular disseminada). O sexto paciente foi a óbito por recidiva da hemorragia digestiva alta. Em nove pacientes, 13,2%, foi diagnosticada trombose da veia porta. Os dados laboratoriais, hematológicos e de função hepática também foram analisados. Conclusões: Os autores concluíram que o tratamento cirúrgico da hipertensão portal esquistossomótica, através da esplenectomia + LVGE + desvascularização da grande curvatura do estômago + esclerose endoscópica pós-operatória determina resultados compatíveis com a literatura em relação à recidiva de sangramento, mas preserva a funcionalidade hepática.Descritores: Esquistossomose hepato-esplênica; Esplenectomia; Trombose da veia porta.

We use the functional renormalization group approach with partial bosonization in the particleparticle channel to study the effect of order parameter fluctuations on the BCS-BEC crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid order parameter at the unitary point and compare our results with experiments and previous calculations.PACS numbers: 03.75.Ss, 03.75.Hh, 74.20.Fg The BCS-BEC crossover in a two-component Fermi gas has attracted the attention of theorists for several decades [1,2,3,4,5]. It is generally accepted that the nature of the superfluid state exhibits a smooth crossover as a function of the dimensionless parameter 1/k F a s , where k F is the Fermi momentum and a s is the s-wave scattering length in vacuum. While for a small negative scattering length, i.e., 1/k F a s ≪ −1, the paired state generated by the attractive interaction is a collection of spatially extended Cooper pairs (BCS limit), in the opposite limit 1/k F a s ≫ 1 the superfluid state can be viewed as a Bose-Einstein condensate of tightly bound fermion pairs (BEC limit). Of particular interest is the unitary point 1/k F a s = 0 where the scattering length diverges and k F sets the only length scale of the system. In this regime quantitative calculations are difficult because there is no small parameter to justify approximations.In the past few years several observables such as the chemical potential and the quasi-particle gap have been determined experimentally at the unitary point [6,7,8,9,10], but there is still some uncertainty in the precise numerical values of these quantities. The unitary point has also been studied theoretically using Monte Carlo simulations [11,12] and various analytical methods based on field theoretical techniques [13,14,15,16,17] or the functional renormalization group (FRG) [18,19,20,21], but also in this case the theoretical results have not converged yet. In such a situation it is desirable to study this problem using new approximation strategies which are complementary to previous calculations. In this work we shall therefore develop a novel FRG approach for the BCS-BEC crossover which is based on a suitable truncation of the vertex expansion using skeleton equations and Ward identities. For fixed density we explicitly calculate the chemical potential, the single-particle gap, and the superfluid order-parameter at the unitary point in three dimensions, and compare our results with experiments and with previous calculations.We consider a system of neutral fermions with energy dispersion ǫ k = k 2 /(2m) and a short-range attractive two-body interaction g p depending on the total momentum p of a fermion pair. After decoupling the intera...