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

Communications in Theoretical Physics

Conformal Invariance and the Lanczos Method Studies of Ashkin–Teller Quantum chain

Haiyan Zhang, Hongru Ma, Bo-Wei Xu

Published Mar 15, 1995• 0 citations
Publisher

Abstract

The low-lying energy spectrum of quantum Ashkin–Teller chain in the critical region is calculated by using Lanczos method. According to conformal theory, the scaling dimensions and the normalizing factor are obtained from the energy spectrum.
DOI
10.1088/0253-6102/23/2/211

Related papers

Conformal invariance and the Lanczos method studies of a spinning quantum chain

Haiyan Zhang, Hongru Ma, Xu Bo-wei

The low-lying energy spectrum of a spinning quantum chain in the critical region is calculated by using Lanczos method. According to conformal theory, the anomalous dimensions ? and the normalising factor ? are obtained from the energy spectrum. Also a simple derivation of the field theory of the model is given.

Acta Physica Sinica (Overseas Edition)•Mar 1, 1995•0 citations

A New Critical Region of Quantum Ashkin–Teller Chain

Wang ZhiGuo, Haiyan Zhang, Xu Bo-wei

The critical phenomena of the one-dimensional quantum Ashkin–Teller chain are discussed by using the numerical calculation in the quantum conformal field theory. The result shows that there exists a new critical region of the model.

Communications in Theoretical Physics•Sep 15, 1999•1 citation

Conformal anomaly and surface energy for Potts and Ashkin-Teller quantum chains

Chris J. Hamer, G R W Quispel, Murray T. Batchelor

Exact equivalences between the critical quantum Potts and Ashkin-Teller chains and a modified XXZ Heisenberg chain have recently been derived by Alcaraz et al (1987). The leading finite-size corrections to the ground-state energies of these chains are derived using the methods of de Vega and Woynarovich (1985) and Eckle. Exact results are then obtained for the conformal anomaly of each model, and for the surface energy in the case of free boundaries.

Journal of Physics A Mathematical and General•Nov 11, 1987•209 citations

Conformal invariance and the spectrum of theXXZchain

Francisco Castilho Alcaraz, Michael N. Barber, Murray T. Batchelor

Numerical solutions of the Bethe-Ansatz equations for the eigenenergies of XXZ Hamiltonian on very large chains are used to identify, via conformal invariance, the scaling dimensions of various two-dimensional models. With periodic boundary conditions, eight-vertex and Gaussian model operators are found. The scaling dimensions of the Ashkin-Teller and Potts models are obtained by the exact relating of eigenstates of their quantum Hamiltonians to those of the XXZ chain with modified boundary conditions. The irrelevant operators governing the dominant finite-size corrections are also identified.

Physical Review Letters•Feb 23, 1987•170 citations

Some finite-size amplitudes and critical exponents for Potts and Ashkin-Teller quantum chains

Chris J. Hamer, Murray T. Batchelor

Analytic expressions are derived for the leading finite-size corrections to a class of energy eigenvalues of the Potts and Ashkin-Teller quantum chains, making use of their equivalences with a modified XXZ Heisenberg chain. Assuming conformal invariance, exact results are thence obtained for some bulk scaling dimensions and surface exponents in these models.

Journal of Physics A Mathematical and General•Feb 7, 1988•24 citations

Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models

Francisco Castilho Alcaraz, Michael N. Barber, Murray T. Batchelor +2 more

Eigenspectra of the critical quantum Ashkin-Teller and Potts chains with free boundaries can be obtained from that of the XXZ chain with free boundaries and a complex surface field. By deriving and solving numerically the Bethe ansatz equations for such boundaries the authors obtain eigenenergies of XXZ chains of up to 512 sites. The conformal anomaly and surface exponents of the quantum XXZ, Ashkin-Teller, and Potts chains are calculated by exploiting their relations with the mass gap amplitudes as predicted by conformal invariance.

Journal of Physics A Mathematical and General•Dec 21, 1987•523 citations
Numerical solutions of the Bethe-Ansatz equations for the eigenenergies of XXZ Hamiltonian on very large chains are used to identify, via conformal invariance, the scaling dimensions of various two-dimensional models. With periodic boundary conditions, eight-vertex and Gaussian model operators are found. The scaling dimensions of the Ashkin-Teller and Potts models are obtained by the exact relating of eigenstates of their quantum Hamiltonians to those of the XXZ chain with modified boundary conditions. The irrelevant operators governing the dominant finite-size corrections are also identified.
Eigenspectra of the critical quantum Ashkin-Teller and Potts chains with free boundaries can be obtained from that of the XXZ chain with free boundaries and a complex surface field. By deriving and solving numerically the Bethe ansatz equations for such boundaries the authors obtain eigenenergies of XXZ chains of up to 512 sites. The conformal anomaly and surface exponents of the quantum XXZ, Ashkin-Teller, and Potts chains are calculated by exploiting their relations with the mass gap amplitudes as predicted by conformal invariance.