that is expressed via the Virasoro modes $L_{0}$, $\bar L_{0}$ and the central charge $c_{\rm UV}$. The eigenvalues of $H_{0}$ are scaling dimensions of ${\rm CFT}_{\rm UV}$ shifted by $\frac{c_{\rm UV}}{12}$ . Since the state space ${\cal H}_{0}$ of the unperturbed theory on a cylinder is discrete $H$ can be represented by an infinite matrix acting in this space. To regulate the UV divergences we can truncate $H$ to a finite matrix by restricting it to a finite dimensional subspace in ${\cal H}_{0}$. This gives rise to a variety of truncated Hamiltonian techniques in which one numerically calculates the eigenvalues and eigenvectors of the truncated Hamiltonian matrix for various values of the scale set by the circle length $R$. In TCSA the truncated subspace is specified by imposing an upper bound on the scaling dimensions of the allowed states. This upper bound is called the truncation level. The UV divergences show up in the dependence of numerics on the truncation level. This dependence and various improvement techniques have been discussed in [@GW], [@LT_RG], [@HRvR], [@RV].

TCSA has been applied to situations in which a perturbed theory arrives to a non-trivial fixed point (see e.g. [@Cardy_etal], [@GW]). In this case the 