Variational monte carlo study of spin-gapped normal state and bcs-bec crossover in two-dimensional attractive hubbard model

Shun Tamura, Hisatosh Yokoyama

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7 Citations (Scopus)


We study the properties of normal, superconducting (SC), and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable for inducing a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength U=t increases, a first-order spin-gap transition arises at U c ∼ W (W: bandwidth) from a Fermi liquid to a spin-gapped state, which is conductive as a result of the hopping of doublons. In the SC state, we confirm by the analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at approximately Uco∼ U c from a BCS type to a Bose-Einstein condensation (BEC) type, as U=t increases. For U < Uco, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit the behavior of ∼exp(-t=U), as expected from the BCS theory. For U > Uco, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as t2=U / Tc, as expected in a bosonic scheme. In this regime, SC transition is induced by a gain in kinetic energy, in contrast to the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.

Original languageEnglish
Article number064718
JournalJournal of the Physical Society of Japan
Issue number6
Publication statusPublished - 2012 Jun


  • Attractive Hubbard model
  • BCS-BEC crossover
  • CDW
  • Condensate fraction
  • Pseudogap
  • Square lattice
  • Superconductivity
  • Superfluid stiffness
  • Variational Monte Carlo method


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