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: Univ Innsbruck, Inst Quantum Opt, A-6020 Innsbruck, Austria; Univ Innsbruck, Quantum Informat Austrian Acad Sci, A-6020 Innsbruck, Austria; Univ Innsbruck, Inst Theoret Phys, A-6020 Innsbruck, Austria; Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada; Scuola Normale Super Pisa, I-56126 Pisa, Italy; UOS Firenze LENS, CNR INO, I-50019 Sesto Fiorentino, Italy; Univ Bologna, Dipartimento Fis & Astron, I-40127 Bologna, Italy; INFN, I-40127 Bologna, Italy; Penn State Univ, Dept Phys, University Pk, PA 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.

Journal/Review: PHYSICAL REVIEW B

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 F oQuS (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.
KeyWords: Long-range Order; Spin Chains; Renormalization-groups; 2-dimensional Systems; Critical-behavior; Ultracold Gases; Phase-diagrams; Ground-states; Ferromagnetism; Transition
DOI: 10.1103/PhysRevB.91.165136

Citations: 30
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