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

Journal of Physics A Mathematical and General

N=1 superconformal invariance in the six-state quantum chain with free boundary conditions

Gunter Markus Schutz

Published Oct 1, 1987• 4 citations
Publisher

Abstract

The spectrum of a six-state one-dimensional quantum chain with free boundaries at the critical point is studied. Using finite-size scaling and conformal invariance, they find a line in the plane of the coupling constants where the system has N=1 superconformal invariance with c=5/4.
DOI
10.1088/0305-4470/20/14/002

Related papers

Superconformal invariance in the Ashkin-Teller quantum chain with free boundary conditions

G von Gehlen, V. Rittenberg

The finite-size limit of the lower part of the spectrum of the Ashkin-Teller chain with free boundary conditions is studied numerically and interpreted from the point of view of conformal invariance. Several irreducible representations of the Virasoro algebra with the central charge c=1 are identified. For two special values of the coupling constant, higher degeneracies occur and the whole spectrum can be understood in terms of a few irreducible representations of the N=2 superconformal algebra.

Journal of Physics A Mathematical and General•Nov 11, 1986•16 citations

Finite-size scaling spectra in the six-states quantum chains

Gunter Markus Schutz

The finite-size scaling spectra of the six-states quantum chains with D 6 symmetry are studied numerically in the massless phase. At least three values of the central charge c of the Virasoro algebra are found: c=1, 1.25, and 1.3. On the self-dual line, one finds, in the c=1 region, N=2 superconformal invariance. In the c=1.25 region there is a line where N=1 superconformal and Zamolodchikov-Fateev symmetry (1985) is observed. The occurrence of higher symmetries is also discussed.

Journal of Physics A Mathematical and General•Mar 21, 1989•4 citations

Toroidal boundary conditions in n-state quantum chains

P. Chaselon

The author considers one-dimensional n-state quantum chains having as symmetry an Abelian group A of order n (generalised Ising chain). These Hamiltonians depend on 2(n-1) coupling constants. For special values of the coupling constants the symmetry of the quantum chains is larger than A corresponding to a (in general non-Abelian) group G with m elements (m)n). For each element of G he finds explicitly a boundary condition which leaves the Hamiltonian translationally invariant. This problem is relevant in finite-size scaling studies at the critical point of a second-order phase transition.

Journal of Physics A Mathematical and General•Jul 7, 1989•5 citations

Operator content of the Ashkin-Teller quantum chain, superconformal and Zamolodchikov-Fateev invariance. I. Free boundary conditions

Michael Baake, G von Gehlen, V. Rittenberg

Based on numerical analysis, the authors conjecture the operator content of the finite-size limit of the spectra of the Ashkin-Teller model with free boundary conditions. The same operator content is obtained from a Hamiltonian with a four-fermion interaction and a U(1) Kac-Moody Sugawara structure. For some special values of the coupling constant the model exhibits N=2 superconformal and Zamolodchikov-Fateev invariance. The operator content in these cases is expressed in terms of irreducible representations of the corresponding algebras.

Journal of Physics A Mathematical and General•Jun 1, 1987•39 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

Conformal invariance and surface critical behaviour of a quantum chain with three-spin interaction

Ferenc Iglói

An Ising model with three-spin interaction is investigated by finite-size scaling applying free boundary conditions. The surface critical properties of the model were determined by conformal invariance. Taking into account logarithmic corrections the surface critical exponents obtained are in accordance with the four-state Potts values.

Journal of Physics A Mathematical and General•Oct 21, 1987•22 citations
The author considers one-dimensional n-state quantum chains having as symmetry an Abelian group A of order n (generalised Ising chain). These Hamiltonians depend on 2(n-1) coupling constants. For special values of the coupling constants the symmetry of the quantum chains is larger than A corresponding to a (in general non-Abelian) group G with m elements (m)n). For each element of G he finds explicitly a boundary condition which leaves the Hamiltonian translationally invariant. This problem is relevant in finite-size scaling studies at the critical point of a second-order phase transition.
Based on numerical analysis, the authors conjecture the operator content of the finite-size limit of the spectra of the Ashkin-Teller model with free boundary conditions. The same operator content is obtained from a Hamiltonian with a four-fermion interaction and a U(1) Kac-Moody Sugawara structure. For some special values of the coupling constant the model exhibits N=2 superconformal and Zamolodchikov-Fateev invariance. The operator content in these cases is expressed in terms of irreducible representations of the corresponding algebras.
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.