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Investigation of quantum phase transitions using multi-target DMRG methods

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Abstract.

In this paper we examine how the predictions of conformal invariance can be widely exploited to overcome the difficulties of the density-matrix renormalization group near quantum critical points. The main idea is to match the set of low-lying energy levels of the lattice Hamiltonian, as a function of the system’s size, with the spectrum expected for a given conformal field theory in two dimensions. As in previous studies this procedure requires an accurate targeting of various excited states. Here we discuss how this can be achieved within the DMRG algorithm by means of the recently proposed Thick-restart Lanczos method. As a nontrivial benchmark we use an anisotropic spin-1 Hamiltonian with special attention to the transitions from the Haldane phase. Nonetheless, we think that this procedure could be generally valid in the study of quantum critical phenomena.

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Authors and Affiliations

  1. Unitá di ricerca INFM di Bologna, viale Berti-Pichat, 6/2, 40127, Bologna, Italy

    C. Degli Esposti Boschi

  2. Dipartimento di Fisica, Universitá di Bologna, INFM and INFN, via Irnerio, 46, 40126, Bologna, Italy

    F. Ortolani

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  1. C. Degli Esposti Boschi
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  2. F. Ortolani
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Correspondence to C. Degli Esposti Boschi.

Additional information

Received: 20 May 2004, Published online: 5 November 2004

PACS:

75.40.Mg Numerical simulation studies - 05.10.Cc Renormalization group methods - 75.10.Pq Spin chain models

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Degli Esposti Boschi, C., Ortolani, F. Investigation of quantum phase transitions using multi-target DMRG methods. Eur. Phys. J. B 41, 503–516 (2004). https://doi.org/10.1140/epjb/e2004-00344-1

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