Real-space renormalization-group study of the phase diagram of two coupled quantum spin-1/2 chains

Ulrich Schollwöck and David Y. K. Ko
Phys. Rev. B 53, 240 – Published 1 January 1996
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Abstract

We investigate the phase diagram of two coupled quantum spin-1/2 chains, a square ladder, allowing for anisotropies both in the interchain and intrachain coupling, using the recently introduced density-matrix renormalization-group (DMRG) algorithm. We consider open chains up to a length of 2×200, while retaining up to 120 states in the truncated basis of the Hilbert space. The phase diagram is discussed in connection with exact results and bosonization analysis. Numerically, we show that the crossover from the critical behavior of the uncoupled disordered spin-1/2 chain to a gapped quantum liquid sets in for infinitesimal interchain coupling, both for ferromagnetic and antiferromagnetic interchain coupling. The Haldane phase of the coupled chains is, even for small interchain couplings, generically described by the Affleck-Kennedy-Lieb-Tasaki model. We also discuss typical shortcomings of the DMRG for some choices of the interaction parameters. © 1996 The American Physical Society.

  • Received 31 July 1995

DOI:https://doi.org/10.1103/PhysRevB.53.240

©1996 American Physical Society

Authors & Affiliations

Ulrich Schollwöck

  • Service de Physique Théorique, Commissariat à l’Energie Atomique, Saclay, 91191 Gif-sur-Yvette Cedex, France

David Y. K. Ko

  • Department of Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom

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Vol. 53, Iss. 1 — 1 January 1996

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