Many-flavor phase diagram of the (2 + 1)<i>d</i>Gross–Neveu model at finite temperature

Scherer, Daniel D.; Braun, Jens; Gies, Holger

doi:10.1088/1751-8113/46/28/285002

Cited by 19 publications

(20 citation statements)

References 118 publications

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“…Future studies may map out the finite temperature phase diagram and especially the crossover [63] from the quantum critical point to the thermal phase transition in the 2D Ising universality class. The CDW transition of the spinful Dirac fermions [64,65] and many-flavored fermions [66] can also be studied using a similar method. Generalization of the model to include hopping and interactions beyond the nearest neighbors may allow us to address the intriguing question about the emergence [67] and stability of the topological insulating states [68,69] in the presence of interactions.…”

Section: Discussionmentioning

confidence: 99%

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

2014

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Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point = V t 1.356(1) with the critical exponents ν = 0.80(3) and η = 0.302 (7). Compatible results for the transition point are also obtained with infinite projected entangled-pair states.

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Section: Discussionmentioning

confidence: 99%

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

2014

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“…Recent examples of the applications of FRG to pure fermionic field theories include the determination of the fixed point structure of the threedimensional (3D) Thirring model [7,8] and of the 3D Gross-Neveu model [9], also for the case when the fermions interact with an external magnetic field [10]. A thorough discussion of asymptotic safety has been presented for this model [11].…”

Section: Introductionmentioning

confidence: 99%

Local potential approximation for the renormalization group flow of fermionic field theories

Jakovác

Patkós

2013

Phys. Rev. D

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The second functional derivative of the effective potential of pure fermionic field theories is rewritten in a factorized form, which facilitates the evaluation of the renormalization flow rate of the effective action in the Wetterich equation. It is applied to the local potential approximation in cases when the effective potential depends on scalar composites built from the fermions. The procedure is demonstrated explicitly on the example of the N f -flavor Gross-Neveu model and the one-flavor chiral Nambu-Jona-Lasinio model.

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“…In order to resolve this problem we have established a connection between the FRG equation and the celebrated PME, whose self-similar solution represents a nonanalytic FP describing the transition. Its analytical continuation to the postfocusing regime provides a unique mechanism of spontaneous generation of a finite DOS at zero energy [60]. Moreover, it shows that the distribution of fluctuations becomes very broad close to the transition.…”

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confidence: 93%

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

2018

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In the presence of randomness, a relativistic semimetal undergoes a quantum transition towards a diffusive phase. A standard approach relates this transition to the U (N ) Gross-Neveu model in the limit of N → 0. We show that the corresponding fixed point is infinitely unstable, demonstrating the necessity to include fluctuations beyond the usual Gaussian approximation. We develop a functional renormalization group method amenable to include these effects and show that the disorder distribution renormalizes following the so-called porous medium equation. We find that the transition is controlled by a nonanalytic fixed point drastically different from that of the U (N ) Gross-Neveu model. Our approach provides a unique mechanism of spontaneous generation of a finite density of states and also characterizes the scaling behavior of the broad distribution of fluctuations close to the transition. It can be applied to other problems where nonanalytic effects may play a role, such as the Anderson localization transition.Introduction. -The interplay between disorder and quantum fluctuations leads to unique phenomena, the most remarkable being the Anderson localization. After more than half a century of intensive efforts, it remains a topical subject of research with applications to various domains of physics ranging from condensed matter to cold atoms and light propagation [1]. Remarkably, a different type of disorder-driven quantum phase transition was discovered recently when considering waves with a quantum relativistic dispersion relation [2]. This transition happens between a pseudoballistic phase and a diffusive metal as a function of the disorder strength (or the energy). It is predicted to occur in particular in the recently discovered three-dimensional (3D) Weyl [3,4] and Dirac semimetals [5][6][7] in which, respectively, two and four electronic bands cross linearly at isolated points. However we expect these phenomena to be relevant to other relativistic waves beyond condensed matter, such as ultracold atoms [8].In spite of numerous efforts, the understanding of this transition remains elusive. In this Letter we show that the fluctuations of the randomness beyond the standard Gaussian approximation invalidate previous fieldtheoretic descriptions of this transition. A very similar mechanism occurs in the context of the Anderson transition: there discrepancies between the results obtained using renormalization group (RG) and numerical simulations grow with the number of loops [9]. One may attribute them to the existence of infinitely many relevant operators of the associated field theory [10] which destabilize the fixed point (FP) usually considered to describe the transition [11][12][13]. We find that the same problem appears at the new semimetal-diffusive metal transition. We demonstrate how to overcome this obstacle by deriving and solving a functional renormalization group (FRG) for the whole (non-Gaussian) disorder distribution. To our knowledge this solution consti-tutes the only example of an analytical de...

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Many-flavor phase diagram of the (2 + 1)dGross–Neveu model at finite temperature

Cited by 19 publications

References 118 publications

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

Local potential approximation for the renormalization group flow of fermionic field theories

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

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