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%e show that for conforrnally invariant two-dimensional systems, the amplitude of the finite-size corrections to the free energy of an infinitely long strip of width L at criticality is linearly related to the conformal anomaly number c, for various boundary conditions. The result is confirmed by renormalization-group arguments and numerical calculations. It is also related to the magnitude of the Casimir effect in an interacting one-dimensional field theory, and to the low-temperature specific heat in quantum chains.

Quantum chemistry by random walk.

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer. Introduction.-Consider the computation of the dominant eigenvalue of an N Â N matrix, with N so large that the matrix cannot be stored. Transformation methods cannot be used in this case, but one can still proceed with the power method, also known as the projection method, as long as one can compute and store the result of multiplication of an arbitrary vector by the matrix. When, for sufficiently large N, this is no longer feasible, Monte Carlo methods can be used to represent stochastically both the vector and multiplication by the matrix. This suffices to implement the power method to compute the dominant eigenvalue and averages involving its corresponding eigenvector.In this Letter, we propose a hybrid method consisting of numerically exact representation and multiplication in a small deterministic subspace, complemented by stochastic treatment of the rest of the space. This semistochastic projection method combines the advantages of both approaches: it greatly reduces the statistical uncertainty of averages relative to purely stochastic projection while allowing N to be large. These advantages are realized if one succeeds in choosing a deterministic subspace that carries a substantial fraction of the total spectral weight of the dominant eigenstate.Semistochastic projection has numerous potential applications: transfer matrix [1] and quantum Monte Carlo (QMC) [2][3][4] calculations, respectively for classical statistical mechanical and quantum mechanical systems, and the calculation of subdominant eigenvalues [5].In this Letter we apply the semistochastic method to compute the ground state energy of quantum mechanical Hamiltonians represented in a discrete basis. In this context, deterministic projection is known as full configuration interaction (FCI) to chemists and as exact diagonalization to physicists, whereas stochastic projection is the essence of various projector QMC methods [2,3]. Hence, semistochastic projection shall be referred to as the SQMC method. The benefit of the SQMC method over the

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