Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/0010278

Finite size effects in perturbed boundary conformal field theories

Patrick Dorey, Mathias Pillin, Pocklington, A., Ingo Runkel B, Roberto Tateo, G.M.T. Watts

Published Oct 30, 2000• 4 citations
arXivHTMLPDF

Abstract

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.
DOI
10.48550/arxiv.hep-th/0010278

Related papers

Finite size effects in perturbed boundary conformal field theories

Roberto Tateo, Patrick Dorey, Mathias Pillin +3 more

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions.Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.

Non-perturbative Quantum Effects•Sep 25, 2000•6 citations

Finite lattice Bethe ansatz systems and the Heun equation

Patrick Dorey, SUZUKI J, Roberto Tateo

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.

•Jan 1, 2004•0 citations

Boundary Conditions in Conformal Field Theory

John Cardy

<!-- *** Custom HTML *** --> We consider conformal field theories on manifolds with a boundary, and the constraints placed by modular invariance on their partition functions. In particular, the partition functions on an annulus with particular boundary conditions are given by the fusion rules. This leads to a simple derivation of the Verlinde formula. We note the remarkable fact that, for some integrable models, these partition functions have the same form away from criticality, with the modular parameter $q$ of the annulus replaced by a temperature-like variable, and give a partial explanation of this in the case of the Ising model.

Advanced studies in pure mathematics•Jun 17, 2018•17 citations

Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries

Yifan Liu, Haruki Shimizu, Atsushi Ueda +1 more

We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.

arXiv:2405.06891•SciPost Physics•Oct 2, 2024•6 citations

One-point functions in perturbed boundary conformal field theories

Patrick Dorey, Mathias Pillin, Roberto Tateo +1 more

We consider the one-point functions of bulk and boundary fields in the scaling Lee-Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.

•Jul 10, 2000•30 citations

Finite size eects in perturbed boundary conformal eld theories

Patrick Dorey, Mathias Pillin, Andrew Pocklington +3 more

Wediscussthenite-sizepropertiesofasimpleintegrablequantumeldtheoryin1+1di- mensionswith non-trivialboundaryconditions. Novelo-criticalidentities betweencylinderpartition functions of models with diering boundary conditions are derived.

•Jan 1, 2000•0 citations
<!-- *** Custom HTML *** --> We consider conformal field theories on manifolds with a boundary, and the constraints placed by modular invariance on their partition functions. In particular, the partition functions on an annulus with particular boundary conditions are given by the fusion rules. This leads to a simple derivation of the Verlinde formula. We note the remarkable fact that, for some integrable models, these partition functions have the same form away from criticality, with the modular parameter qqq of the annulus replaced by a temperature-like variable, and give a partial explanation of this in the case of the Ising model.
We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.
We consider the one-point functions of bulk and boundary fields in the scaling Lee-Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.