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arXiv:1004.4844 · Journal of Statistical Mechanics Theory and Experiment

Energy level distribution of perturbed conformal field theories

Giuseppe Piero Brandino, Robert Konik, Giuseppe Mussardo

Published Jul 23, 2010• 43 citations
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Abstract

We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable.We compute their spectrum using a renormalization group improved truncated conformal spectrum approach.With this method we are able to study systems where more than 40 000 states are kept and where we determine the energies of the lowest several thousand eigenstates with high accuracy.We find, as expected, that the level spacing statistics of integrable perturbed minimal models are Poissonian while the statistics of nonintegrable perturbations are GOE-like.However, by varying the system size (and so controlling the positioning of the theory between its IR and UV limits) one can induce crossovers between the two statistical distributions.

DOI
10.1088/1742-5468/2010/07/p07013

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The finite-volume spectrum of an integrable massive perturbation of a rational conformal field theory interpolates between massive multiparticle states in infinite-volume (IR limit) and conformal states, which are approached at zero volume (UV limit). Each state is labeled in the IR by a set of “Bethe-ansatz quantum numbers,” while in the UV limit it is characterized primarily by the conformal dimensions of the conformal field creating it. We present explicit conjectures for the UV conformal dimensions corresponding to any IR state in the ϕ1, 3-perturbed minimal models ℳ(2, 5) and ℳ(3, 5). The conjectures, which are based on a combinatorial interpretation of the Rogers-Ramanujan-Schur identities, are consistent with numerical results obtained previously for low-lying energy levels.
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