Rapidly-converging Methods for the Location of Quantum Critical Points from Finite-size Data

We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of thermodynamic observables toward the infinite-size limit. After the identification and cancellation of the terms that are responsible for the leading power-law scaling, we are able to obtain sequences of pseudo-critical points governed by next-to-leading terms which display larger shift exponents as compared to currently used methods, in particular the so-called Phenomenological Renormalization Group [1] that is still the common choice for the location of quantum critical points. Similarly, we are also able to improve our recent Finite-Size Crossing Method [2]. Our new approach [3] is valid in any spatial dimension and for any value of the dynamic exponent. We demonstrate the effectiveness of our methods both analytically on the basis of the one-dimensional XY model in transverse field, and numerically considering c=1 transitions occurring in non integrable spin models, which are also relevant in the context of quantum information theory due to their entanglement features. In particular, we show how the Homogeneity Condition Method is able to locate the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state properties on relatively small systems. [1] M. N. Barber in Phase transitions and critical phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1983), vol. 8. [2] L. Campos Venuti, C. Degli Esposti Boschi, M. Roncaglia and A. Scaramucci, Phys. Rev. A 73, 010303(R) (2006). [3] M. Roncaglia, L. Campos Venuti and C. Degli Esposti Boschi, Phys. Rev. B 77, 155413 (2008).