Quantum critical behavior in three dimensional lattice Gross-Neveu models

Chandrasekharan, Shailesh; Li, Anyi

doi:10.1103/physrevd.88.021701

Cited by 79 publications

(121 citation statements)

References 52 publications

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“…In previous studies it was possible to use Eq. (34) by expanding f (x) in a power series up to x 4 , and fit the Monte Carlo data to it and thus extract the critical coupling and exponents [43,51]. Unfortunately, in our current study such an analysis seems to be quite unstable.…”

Section: Analysis and Resultsmentioning

confidence: 99%

“…We locate the critical point with an error of about a percent. Although we were able to perform calculations up to lattice sizes of L = 28, scaling seems to set in only for L ≥ 20, unlike other staggered fourfermion models that were solved recently, where the data begin to show scaling behavior even for L ≥ 12 [43,51]. For this reason we were only able to bound the critical exponents within a range.…”

Section: Discussionmentioning

confidence: 99%

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Massive fermions without fermion bilinear condensates

Ayyar

Chandrasekharan

2015

Phys. Rev. D

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We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a SU (4) symmetry which forbids nonzero fermion bilinear mass terms, due to which there is a massless fermion phase at weak couplings. However, even at strong couplings fermion bilinear condensates do not appear in our model, although fermions do become massive. While the existence of this exotic strongly coupled massive fermion phase was established long ago, the nature of the transition between the massless and the massive phase has remained unclear. Using Monte Carlo calculations in three space-time dimensions, we find evidence for a direct second order transition between the two phases suggesting that the exotic lattice phase may have a continuum limit at least in three dimensions. A similar exotic second order critical point was found recently in a bilayer system on a honeycomb lattice.

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Section: Analysis and Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Massive fermions without fermion bilinear condensates

Ayyar

Chandrasekharan

2015

Phys. Rev. D

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“…In fact, there is a substantial body of literature on such models as they can give rise to critical phenomena where -in addition to the dimension and the symmetry of the (bosonic) order parameter -also the number and structure of the (fermionic) long-range degrees of freedom characterize the universal properties. Their quantitative determination has been pursued by a variety of methods including and 1/N expansions [16][17][18][19][20][21][22][23][24], Monte-Carlo simulations [17,[25][26][27][28][29][30][31][32][33], as well as the functional RG [34][35][36][37][38][39][40][41]. These models have recently received a great deal of attention as effective models describing phase transitions from a disordered (e.g., semi-metallic) to an ordered (e.g., Mott-insulating or superconducting) phase [2-4, 42, 43] In the present work, we investigate the emergence of supersymmetry in a (2+1) dimensional Yukawa-type model with a single Majorana fermion and a dynamical real scalar order parameter field.…”

Section: Jhep12(2017)132mentioning

confidence: 99%

A functional perspective on emergent supersymmetry

Gies

Hellwig

Wipf

et al. 2017

J. High Energ. Phys.

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Abstract:We investigate the emergence of N = 1 supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the -expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.

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“…The quantum critical behavior of this transition for N = 2 has previously been accessed by different approaches, most recently by higherorder perturbative and non-perturbative RG calculations and Majorana Quantum Monte Carlo simulations: For the purely fermionic Gross-Neveu model expanded in D = 2 + ǫ dimensions the RG functions are known to order ǫ 4 and for ǫ = 1 yield an inverse correlation length exponent 1/ν ≈ 0.931 after resummation [24], while the most sophisticated non-perturbative functional RG calculation gives a value of 1/ν ≈ 0.994(2) [25]. Novel lattice methods have managed to access the question avoiding the sign problem, but predicting a rather different value of 1/ν ≈ 1.20(1) [28]. We show a numerical evaluation of Eq.…”

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Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems

et al. 2017

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Dirac and Weyl fermions appear as quasi-particle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu model. In this work we study the bosonized version of the standard Gross-Neveu model -the Gross-Neveu-Yukawa theory -at three-loop order, and compute critical exponents in 4−ǫ dimensions for general number of fermion flavors. Our results fully encompass the previously known two-loop calculations, and agree with the known three-loop results in the purely bosonic limit of the theory. We also find the exponents to satisfy the emergent super-scaling relations in the limit of a single-component fermion, order by order up to three loops. Finally, we apply the computed series for the exponents and their Padé approximants to several phase transitions of current interest: metal-insulator transitions of spin-1/2 and spinless fermions on the honeycomb lattice, emergent supersymmetric surface field theory in topological phases, as well as the disorder-induced quantum transition in Weyl semimetals. Comparison with the results of other analytical and numerical methods is discussed.Introduction. Dirac and Weyl fermions are an abundant form of quasi-particle excitations in condensed matter physics[1, 2] appearing in very different materials ranging from graphene, via d-wave superconductors, to the surface states of topological insulators, or even three-dimensional (3D) materials such as Na 3 Bi and Cd 3 As 2 [3,4]. While the physical origin of the quasirelativistic energy dispersion can be quite different in various materials, it leads to universal low-energy properties shared by all these materials, such as, e.g., the density of states (DOS) and the concomitant thermodynamic properties or various response functions. Dirac and Weyl systems can also undergo transitions from their natural semi-metallic phase to a variety of broken symmetry phases as some parameter is varied. This includes continuous quantum transitions to interaction-induced, ordered, many-body ground states[5-10] and a disorderdriven transition to a diffusive state with finite DOS [11][12][13][14][15][16]. Depending on the broken symmetry of the ordered phase and the fermionic content, the corresponding transition represents a universality class with the concomitant critical behavior. Various of these transitions have been suggested to belong to the universality class defined by the chiral transition appearing in the 3D GrossNeveu (GN) model [7] well-known in the context of highenergy physics and conformal field theories [17,18]. This applies, in particular, to the interaction-induced transition toward a charge density wave of electrons on the 2D honeycomb lattice that breaks the (Ising) sublattice symmetry [7], or the disorder-driven transition toward a diffusive metal in a 3D Weyl semi-metal [15].

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Quantum critical behavior in three dimensional lattice Gross-Neveu models

Cited by 79 publications

References 52 publications

Massive fermions without fermion bilinear condensates

Massive fermions without fermion bilinear condensates

A functional perspective on emergent supersymmetry

Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems

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