Conformal boundary state for the rectangular geometry

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

doi:10.1016/j.nuclphysb.2012.04.021

Cited by 22 publications

(48 citation statements)

References 32 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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“…Finally, certain overlaps with low energy eigenstates in the gapless phase |∆ f | < 1 can be studied using field-theoretical methods. In particular, subleading terms in such overlaps [134][135][136] allow to access universal data about the underlying conformal field theory. Our focus here, in contrast, has been on the full spectrum, not just low-energy physics.…”

Section: Discussionmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

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“…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%

“…To conclude this section, let us recast our result (18) in a more general form, valid for any simply connected domain with several corner of angle 2π (we will later consider specific examples of such domains). This more general form can be obtained by relaxing the condition (16), and by repeating the same arguments as above.…”

Section: Logarithmic Correction In the Case θ = 2πmentioning

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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Conformal boundary state for the rectangular geometry

Cited by 22 publications

References 32 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

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

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

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