Fermion-induced quantum criticality with two length scales in Dirac systems

Torres, Emilio Mínguez; Claßen, Laura; Herbut, Igor F.; Scherer, Michael M.

doi:10.1103/physrevb.97.125137

Cited by 40 publications

(38 citation statements)

References 91 publications

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“…With the Borel resummation described in Sec. V applied to the 4 − expansion of the GNY model, we obtain the critical exponents 1/ν ≈ 0.993 (27), η φ ≈ 0.704 (15) and η ψ ≈ 0.043 (12). This compares very well with the perturbative RG estimates which we obtained using the combination of 2+ and 4− expansions in terms of the two-sided Padé approximants, Sec.…”

Section: B Graphene Case (N = 8)supporting

confidence: 85%

Critical behavior of Dirac fermions from perturbative renormalization

2018

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Gapless Dirac fermions appear as quasiparticle excitations in various condensed-matter systems. They feature quantum critical points with critical behavior in the 2+1 dimensional Gross-Neveu universality class. The precise determination of their critical exponents defines a prime benchmark for complementary theoretical approaches, such as lattice simulations, the renormalization group and the conformal bootstrap. Despite promising recent developments in each of these methods, however, no satisfactory consensus on the fermionic critical exponents has been achieved, so far. Here, we perform a comprehensive analysis of the Ising Gross-Neveu universality classes based on the recently achieved four-loop perturbative calculations. We combine the perturbative series in 4 − spacetime dimensions with the one for the purely fermionic Gross-Neveu model in 2+ dimensions by employing polynomial interpolation as well as two-sided Padé approximants. Further, we provide predictions for the critical exponents exploring various resummation techniques following the strategies developed for the three-dimensional scalar O(n) universality classes. We give an exhaustive appraisal of the current situation of Gross-Neveu universality by comparison to other methods. For large enough number of spinor components N ≥ 8 as well as for the case of emergent supersymmetry N = 1, we find our renormalization group estimates to be in excellent agreement with the conformal bootstrap, building a strong case for the validity of these values. For intermediate N as well as in comparison with recent Monte Carlo results, deviations are found and critically discussed. arXiv:1806.04977v1 [cond-mat.str-el]

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Section: B Graphene Case (N = 8)supporting

confidence: 85%

Critical behavior of Dirac fermions from perturbative renormalization

2018

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“…As there is an emergent continuous U(1) at the QCP (see Fig. 2(a)), the critical behavior of the SM with chiral Dirac fermions to KVBS phase transition might be described by the chiral XY universality class [24,25,[28][29][30][31]33]. To confirm this conjecture, we perform a finite size scaling of the KVBS structure factor near the QCP, and make a data collapse to find the critical exponents.…”

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confidence: 89%

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

2018

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Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.

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“…Study of quantum critical points in these four-fermion models has reemerged as an exciting area of research [15], especially due to the recent discovery that many materials can be described by Dirac fermions in the low energy limit and such materials can have new phases and quantum critical points that separate them [16,17]. Massless fermions can even help induce new quantum critical points and multi-critical points that do not exist in purely bosonic models [18][19][20][21]. New analytical studies of the Gross-Neveu transitions using -expansions [22][23][24], large-N expansions [25,26], functional renormalization group techniques [27] and the bootstrap approach [28] have been performed recently.…”

Section: Introductionmentioning

confidence: 99%

Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

Huffman

Chandrasekharan

2020

Phys. Rev. D

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Motivated by the fermion bag approach we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points. As a test of our method we construct the partition function of a simple lattice Hamiltonian in 2 + 1 dimensions in discrete time, with a temporal lattice spacing ε. When ε → 0 we obtain the partition function of the original lattice Hamiltonian. But when ε = 1 we obtain a new type of space-time lattice field theory which treats space and time differently. Here we show that both continuous-time and discrete-time lattice models have a fermionic quantum critical point with critical exponents that match within errors. The fermion bag algorithms run relatively faster on the discrete-time model and allow us to compute quantities even on 100 3 lattices near the quantum critical point.

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Fermion-induced quantum criticality with two length scales in Dirac systems

Cited by 40 publications

References 91 publications

Critical behavior of Dirac fermions from perturbative renormalization

Critical behavior of Dirac fermions from perturbative renormalization

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

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