two-dimensional Euclidean quantum field theories. We will look at flows that originate in a UV fixed point described by a 2D ${\rm CFT}_{\rm UV}$ and arrive at an IR fixed point described by a ${\rm CFT}_{\rm IR}$ which may be trivial if a mass gap develops along the flow. The flows are triggered by perturbations of ${\rm CFT}_{\rm UV}$ by relevant operators $\phi_{i}$. In general it is a hard non-perturbative problem to determine the infrared properties of the perturbed theory, in particular to identify ${\rm CFT}_{\rm IR}$ when it is non-trivial. A technique that allows one to investigate the perturbed theories numerically in the infrared including the flows to non-trivial fixed points is the truncated conformal space approach (TCSA) invented in [@YZ1], [@YZ2]. The basic setup of TCSA is as follows.

In order not to worry about perturbative infrared divergences we put the perturbed theory on a cylinder with spacial periodic coordinate $x\sim x+ R$ and Euclidean time $y$ directed along the axis of the cylinder. In the Hamiltonian formalism the perturbed Hamiltonian on a circle at $y=0$ is \[Ham\_pert\] H=H\_[0]{} + \^[i]{} dx \_[i]{}(x,0) . Here H\_[0]{}=( L\_[0]{} + |L\_[0]{} - ) is the Hamiltonian of ${\rm CFT}_{\rm UV}$ 