Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models

Year: 2015

Authors: Dalmonte M., Carrasquilla J., Taddia L., Ercolessi E., Rigol M.

Autors Affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria;
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5;
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy, and CNR-INO, UOS di Firenze LENS, Via Carrara 1, 50019 Sesto Fiorentino, Italy;
Dipartimento di Fisica e Astronomia, Universita’ di Bologna and INFN, via Irnerio 46, 40127 Bologna, Italy;
Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

Abstract: We discuss how to locate critical points in the Berezinskii-Kosterlitz-Thouless (BKT) universality class by means of gap-scaling analyses. While accurately determining such points using gap extrapolation procedures is usually challenging and inaccurate due to the exponentially small value of the gap in the vicinity of the critical point, we show that a generic gap-scaling analysis, including the effects of logarithmic corrections, provides very accurate estimates of BKT transition points in a variety of spin and fermionic models. As a first example, we show how the scaling procedure, combined with density-matrix-renormalization-group simulations, performs extremely well in a nonintegrable spin-3/2 XXZ model, which is known to exhibit strong finite-size effects. We then analyze the extended Hubbard model, whose BKT transition has been debated, finding results that are consistent with previous studies based on the scaling of the Luttinger-liquid parameter. Finally, we investigate an anisotropic extended Hubbard model, for which we present the first estimates of the BKT transition line based on large-scale density-matrix-renormalization-group simulations. Our work demonstrates how gap-scaling analyses can help to locate accurately and efficiently BKT critical points, without relying on model-dependent scaling assumptions.


Volume: 91 (16)      Pages from: 165136-1  to: 165136-8

More Information: We thank C. Degli Esposti Boschi and F. Ortolani for help with the DMRG code. M.D. was supported by the ERC Synergy Grant UQUAM, SIQS, and SFB FoQuS (FWF Project No. F4016-N23). J.C. acknowledges support from the John Templeton Foundation. Research at Perimeter Institute is supported through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. L.T. acknowledges financial support from the EU integrated project SIQS. E.E. acknowledges the INFN grant QUANTUM for partial financial support. M.R. was supported by the National Science Foundation, Grant No. PHY13-18303.
DOI: 10.1103/PhysRevB.91.165136

Citations: 28
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