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تسجيل مستخدم جديدThe renormalisation group for the truncated conformal space approach on the cylinder
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In this paper we continue the study of the truncated conformal space approach to perturbed conformal field theories, this time applied to bulk perturbations and focusing on the leading truncation-dependent corrections to the spectrum. We find expressions for the leading terms in the ground state energy divergence, the coupling constant renormalisation and the energy rescaling. We apply these methods to problems treated in two seminal papers and show how these RG improvements greatly increase the predictive power of the TCSA approach. One important outcome is that the TCSA spectrum of excitations is predicted not to converge for perturbations of conformal weight greater than 3/4, but the ratios of excitation energies should converge.
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In this paper we continue the study of the truncated conformal space approach to perturbed boundary conformal field theories. This approach to perturbation theory suffers from a renormalisation of the coupling constant and a multiplicative renormalis
ation of the Hamiltonian. We show how these two effects can be predicted by both physical and mathematical arguments and prove that they are correct to leading order for all states in the TCSA system. We check these results using the TCSA applied to the tri-critical Ising model and the Yang-Lee model. We also study the TCSA of an irrelevant (non-renormalisable) perturbation and find that, while the convergence of the coupling constant and energy scales are problematic, the renormalised and rescaled spectrum remain a very good fit to the exact result, and we find a numerical relationship between the IR and UV couplings describing a particular flow. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points.
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In this paper we consider excited state g-functions, that is, overlaps between boundary states and excited states in boundary conformal field theory. We find a new method to calculate these overlaps numerically using a variation of the truncated conf
ormal space approach. We apply this method to the Lee-Yang model for which the unique boundary perturbation is integrable and for which the TBA system describing the boundary overlaps is known. Using the truncated conformal space approach we obtain numerical results for the ground state and the first three excited states which are in excellent agreement with the TBA results. As a special case we can calculate the standard g-function which is the overlap with the ground state and find that our new method is considerably more accurate than the original method employed by Dorey et al.
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