A study of asymptotic behaviour in the Truncated Conformal Space Approach
Mc Ateer, Dermot
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The Truncated Conformal Space Approach (TCSA) is a numerical technique for calculating the spectrum of Hamiltonian operators in Quantum Field Theory which are described as perturbations of Conformal Field Theories. The truncation errors of the method have been systematically studied near the UV fixed point (when the characteristic energy related to the coupling is less than the truncation cut-off) where a good theoretical understanding has been achieved. However, numerically the method has also demonstrated a good agreement with other results for much larger values of the coupling, when the RG flow approaches a new fixed point in the infrared. We investigate this regime for a number of boundary RG flows, testing the leading exponent and truncation errors. We study the ‘flows beyond’ the first fixed point which have been observed numerically but yet lack a theoretical understanding. We show that while in some models such flows approximate reversed physical RG flows, in others, the spectrum approaches a stable regime that does not correspond to any local boundary condition. In certain examples, multiple fixed points are passed as we increase the coupling. We consider perturbations by irrelevant operators in an effort to control the qualitative behaviour of these flows and offer an explanation for their origin. Furthermore we find that in general the flows beyond the first fixed point are very sensitive to modifications of the truncation scheme. We consider modified truncation schemes both within and outwith the Truncated Conformal Space Approach to investigate these effects.