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Physical review. B, Condensed matter

Phase diagram of the Ashkin-Teller quantum spin chain

Masanori Yamanaka, Yasuhiro Hatsugai, Mahito Kohmoto

Published Jul 1, 1994• 15 citations
Publisher

Abstract

We study a one-dimensional quantum Hamiltonian which is related to a highly anisotropic version of the two-dimensional Ashkin-Teller model. We explore the parameter region and complete its ground-state phase diagram. This problem is studied by using duality relations and by series expansions up to seventeenth order. Corresponding critical indices are also calculated. In this parameter region, a line of continuously varying critical indices is found.

DOI
10.1103/physrevb.50.559

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We study a one-dimensional quantum Hamiltonian which is related to a highly anisotropic version of the two-dimensional Ashkin-Teller model. We explore the parameter region and complete its ground-state phase diagram. This problem is studied by using duality relations and by series expansions up to seventeenth order. Corresponding critical indices are also calculated. In this parameter region, a line of continuously varying critical indices is found.
We study a one-dimensional quantum Hamiltonian problem which is equivalent to a highly anisotropic version of the two-dimensional Ashkin-Teller model. This problem is studied by using its duality and other symmetry properties, by a consideration of its limiting cases, and by mapping it into an XXZ\mathrm{XXZ}XXZ linear chain which is equivalent to a highly anisotropic six-vertex model. In addition eleventh-order strong-coupling series are used to derive numerical data about the Hamiltonian problem. By these means a phase diagram is obtained. The essentially new feature of this diagram is a "critical fan," i.e., a region where a line of continuously varying criticality "fans out" and becomes an area of critical behavior.
The phase diagram and the critical properties of the Hamiltonian version of the two-dimensional n-component cubic model are investigated. Judging from the results of simple limits, mean-field calculation and RG transformations, the phase diagram of the one-dimensional quantum system is similar to that of the two-dimensional classical model. Several RG transformations were used to investigate the critical properties using different cell sizes in the transformation. The coincidence of critical and tricritical fixed points and the presence of a marginal operation showed the formation of the Ashkin-Teller fixed line and the breaking of the universality. The cubic transition is found to be first order for n>2.