Rectangular amplitudes, conformal blocks, and applications to loop models

Bondesan, Roberto; Jacobsen, Jesper Lykke; Saleur, Hubert

doi:10.1016/j.nuclphysb.2012.10.018

Cited by 18 publications

(30 citation statements)

References 37 publications

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“…This was verified in our previous work on the square lattice and triangular lattice with free BCs [19,20]. Later on, Imamura et al study the corner terms with different BCs within CFT [25][26][27]. According to their results, the contribution to the free energy from a corner with two edges under α and β BCs f corn (αβ) is given by…”

Section: Critical Two-dimensional Ising Modelsupporting

confidence: 60%

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Critical two-dimensional Ising model with free, fixed ferromagnetic, fixed antiferromagnetic, and double antiferromagnetic boundaries

Izmailyan

2015

Phys. Rev. E

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Original citation:Wu, Xintian and Izmailyan, N. (2015) Publisher:American Physical Society Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. The critical two-dimensional Ising model is studied with four types boundary conditions: free, fixed ferromagnetic, fixed antiferromagnetic, and fixed double antiferromagnetic. Using bond propagation algorithms with surface fields, we obtain the free energy, internal energy, and specific heat numerically on square lattices with a square shape and various combinations of the four types of boundary conditions. The calculations are carried out on the square lattices with size N × N and 30 < N < 1000. The numerical data are analyzed with finite-size scaling. The bulk, edge, and corner terms are extracted very accurately. The exact results are conjectured for the corner logarithmic term in the free energy, the edge logarithmic term in the internal energy, and the corner logarithmic term in the specific heat. The corner logarithmic terms in the free energy agree with the conformal field theory very well. CURVE is the Institutional Repository for Coventry University

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Section: Critical Two-dimensional Ising Modelsupporting

confidence: 60%

“…Through fitting the data, we get very accurate expansions of the free energy, internal energy, and specific heat. The corner logarithmic corrections in the free energy verify the conformal field theory (CFT) predictions [25][26][27]. The exact edge and corner logarithmic terms in the internal energy and specific heat are conjectured.…”

Section: Introductionsupporting

confidence: 59%

Critical two-dimensional Ising model with free, fixed ferromagnetic, fixed antiferromagnetic, and double antiferromagnetic boundaries

Izmailyan

2015

Phys. Rev. E

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“…However, these contributions appear both in the numerator and the denominator of (A. 19), and they all cancel. The next leading contribution is of order O(log L) is a conformal field theory; it is the free energy f cone that comes from the conical singularity in the world-sheet.…”

Section: Appendix A4 Orthogonality Catastrophesmentioning

confidence: 99%

“…The study of statistical systems in the presence of corner singularities is a topic that is interesting in its own right [17,18,19,20,21,22,23,24]. In this paper, we focus on the subleading corrections to the corner free energies in two-dimensional critical systems, beyond the leading order of Cardy and Peschel [17].…”

Section: Universality and Free Energiesmentioning

confidence: 99%

Logarithmic corrections to the free energy from sharp corners with angle 2π

Stéphan¹,

Dubail²

2013

J. Stat. Mech.

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Abstract. We study subleading corrections to the corner free energy in classical two-dimensional critical systems, focusing on a generic boundary perturbation by the stress-tensor of the underlying conformal field theory (CFT). In the particular case of an angle 2π, we find that there is an unusual correction of the form L −1 log L, where L is a typical length scale in the system. This correction also affects the one-point function of an operator near the corner. The prefactor can be seen as semi-universal, in the sense that it depends on a single non-universal quantity, the extrapolation length. Once this ultraviolet cutoff is known, the term is entirely fixed by the geometry of the system, and the central charge of the CFT. Such a corner appears for example in the bipartite fidelity of a one-dimensional quantum system at criticality, which allows for several numerical checks in free fermions systems. We also present an exact result in the XX and Ising chains that confirms this analysis. Finally, we consider applications to the time evolution of the (logarithmic) Loschmidt echo and the entanglement entropy following a local quantum quench. Due to subtle issues in analytic continuation, we find that the logarithmic term in imaginary time transforms into a time-dependent L −2 correction for the entanglement entropy, and a L −2 log L term for the Loschmidt echo.

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“…The nicest formulas here occur for a rectangle split into two rectangles, where there are at most two places where the boundary condition changes. In this case, the partition function for an L x × L y rectangle is known for all CFTs [13][14][15]:…”

Section: (C)mentioning

confidence: 99%

Geometric Mutual Information at Classical Critical Points

et al. 2014

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A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly (c/3) ln for an interval of length in an infinite system, where c is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2d conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to c. This makes it possible to extract c in classical simulations, which we demonstrate for the critical Ising and 3-state Potts models. Introduction.-In studies of new and exotic phases of quantum matter, the entanglement entropy has established itself as an important resource [1]. It is particularly useful in the many 1d quantum critical systems governed by a conformal field theory (CFT) [2] in the large-distance limit. Here the Rényi entanglement entropy S n of the ground-state is universal [3][4][5][6], and the leading piece is proportional to the central charge c of the CFT characterizing the universality class. Namely, for a periodic system of length L cut into two open segments of respective sizes L A and L B = (L − L A ),

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Rectangular amplitudes, conformal blocks, and applications to loop models

Cited by 18 publications

References 37 publications

Critical two-dimensional Ising model with free, fixed ferromagnetic, fixed antiferromagnetic, and double antiferromagnetic boundaries

Critical two-dimensional Ising model with free, fixed ferromagnetic, fixed antiferromagnetic, and double antiferromagnetic boundaries

Logarithmic corrections to the free energy from sharp corners with angle 2π

Geometric Mutual Information at Classical Critical Points

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