Pinning the order: The nature of quantum criticality in the hubbard model on honeycomb lattice

Physical Review X

Volumn 3, Issue 3, 2014, Pages

  Assaad, Fakher F ^a,c   Herbut, Igor F ^b,c  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b SIMON FRASER UNIVERSITY   (Canada)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETIC STATE; AUXILIARY-FIELD QUANTUM MONTE CARLO; ENHANCED RESOLUTIONS; FINITE SIZE SCALING; QUANTUM CRITICALITY; QUANTUM PHASE TRANSITIONS; SYMMETRY-BREAKING FIELD; TWO-POINT CORRELATION FUNCTION;

HONEYCOMB STRUCTURES; PHASE TRANSITIONS;

HUBBARD MODEL;

EID: 84893630448     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.3.031010     Document Type: Article

References (23)

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16. Clearly, one cannot exchange the limits in Eq. (6). However, one can measure the magnetization at the largest distance available on the lattice, thereby tying together the thermodynamic and infinite distances from the pinning center limits. This procedure can lead to spurious results.
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19. Here, large means comparable to the bandwidth. If the pinning field is much larger than the bandwidth, charge fluctuations on the pinning site will be blocked by an energy scale set by h0. Thereby, in the limit h0 !1, the pinning site effectively drops out of the Hamiltonian and no symmetry breaking occurs. The very slight drop in the magnetization at h0 1/4 5 and on small lattices in Fig. 1(a) could be a precursor of this effect.
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21. In Ref. [1], a small but finite spin gap with maximal value at U/t = 4 was reported. The spin gap is determined with the same method as the single-particle gap, by fitting the tail of the imaginary time-displaced spin-spin correlation functions to a single exponential. Enhancing the imaginary time range for the fit produces a slight decrease of the spin gap for the larger lattices sizes. This slight decrease renders the extrapolation to the thermodynamic limit inconclusive.
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