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Using diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at T = 0. We find clear evidence of an excitonic condensate, whose stability however is affected by an in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or interlayer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low-order density matrices to give a microscopic characterization of correlations as well as to try and estimate the condensate fraction.

We have evaluated the density-density static response of a many-body system by calculating with the quantum Monte Carlo method the energy and density change caused by an external potential. Our results for the linear response function of liquid ^He at zero pressure and temperature are in excellent agreement with the available experimental data. The results for the response function of 2D electrons also at zero temperature, obtained within the fixed-node approximation, constitute the most accurate information available to date for this system. PACS numbers: 05.30.-d, 02.50.-l-sThe quantum Monte Carlo method (QMC) provides a systematic route to the calculation of exact properties of many-body systems [1]. For bosons, in particular, stable algorithms exist that yield virtually exact results [2,3]. This is not the case with fermions, which suffer from the so-called sign problem. However, very accurate results have been obtained for a number of systems, ranging from the homogeneous electron fluid [4,5], to light molecules [6], and to solid hydrogen [7], using the fixednode approximation. The vast majority of calculations to date have been for equilibrium properties such as energy, one-particle-orbital occupation numbers, and static correlation functions. Calculations of time-dependent correlation functions and of the related response functions [8] have been lacking for continuum systems. With the exception of some recent progress [9] for lattice models, the same lack of results holds for the static response functions which are properties of the many-body system that, apart from their intrinsic interest, are of importance to density functional developments beyond LDA [10] and crucial to the recently developed theory of quantum freezing [11].We show that the static density-density response function is directly calculable by QMC with little increase in technical complexity as compared with other properties. We directly use the definition of static response function, rather than evaluate it in terms of the time-dependent correlations, via the fluctuation-dissipation theorem [8]. We apply a static external potential, '^ext(r) = 2t;qCOs(q-r),which induces a modulation of the density with respect to its mean value, no. Such a modulation contains periodic components at all wave vectors that are nonvanishing integer multiples of q. In particular, one finds a modulation with wave vector q, ni(r) = 2nqCos(q • r), wherespace. Similarly the ground-state energy (per particle) can be expanded in even powers of v^:only contains odd powers of t^q. Here X(Q) denotes the static density-density linear response function in FourierThe coeSicients C3 and C4 in the above equations are determined by the cubic response function [12]. QMC allows the direct evaluation of both nq and Ey^ for given q and fq. We perform simulations at a few coupling strengths v^ and then extract X{Q) ^S well as the higherorder response functions from the calculated nq or Ey, by fitting in powers of t'q. As an illustration, we have chosen to study superfluid "^He an...