From Luttinger liquid to Mott insulator: the correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach

Abstract

We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t-J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct power-law behavior of the correlation functions, with the exponents predicted by the Tomonaga-Luttinger theory. By decreasing the doping, the insulating phase is reached with a continuous change of the small-$q$ part of the Jastrow factor.

arXiv comment7 pages, 9 figures

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• Mott correlated states in the underdoped two-dimensional Hubbard model: variational Monte Carlo versus a dynamical cluster approximation
• Mott transition in bosonic systems: Insights from the variational approach
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• Long-Range Entangled-Plaquette States for Critical and Frustrated Quantum Systems on a Lattice
• Ground state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model
• Interaction induced Fermi-surface renormalization in the $t_1-t_2$ Hubbard model close to the Mott-Hubbard transition
• Failure of Gutzwiller-type wave function to capture gauge fluctuations: Case study in the Exciton Bose Liquid context
• Improved Multi-Variable Variational Monte Carlo Method Examined by High-Precision Calculations of One-Dimensional Hubbard Model
• Spinon and eta-spinon correlation functions
• Exact Jastrow-Slater wave function for the one-dimensional Luttinger model
• Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension