Fermion-induced quantum critical points

Li, Zixiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

doi:10.1038/s41467-017-00167-6

Cited by 124 publications

(159 citation statements)

References 60 publications

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“…Further, the case N ¼ 2 is relevant to a Kekulé valence bond solid transition in graphene [52][53][54] which is described by a complex order parameter, however, with a discrete Z 3 symmetry. In the this scenario it was argued that at the QCP the Z 3 gets enhanced to an emergent Uð1Þ symmetry leading to a set of critical exponents that is shared with the N ¼ 2 chiral XY model [55][56][57]. Another intriguing scenario where the chiral XY model is relevant are the surface states of three-dimensional topological insulators where emergent supersymmetry has been conjectured at the quantum critical point [43,46,58].…”

Section: B Chiral Xy Modelmentioning

confidence: 99%

“…As before, we only give the results for the Padé approximants P ½2=2 and P ½3=1 which, in the case of the chiral XY model, do not show any poles for D ∈ f2; 4g for investigated values of N. In Table II, we also provide the estimates from the functional RG [57] and recent quantum Monte Carlo calculations [55]. Again, the results for the inverse correlation length exponent agree reasonably well within the different RG approaches, however, there is a rather large difference when compared to the QMC results.…”

Section: B Chiral Xy Modelmentioning

confidence: 99%

“…Further, the case N ¼ 2 is relevant to a Kekulé transition in graphene [52][53][54][55] which is described by a complex Z 3 order parameter [56,57], however, exhibits emergent Uð1Þ symmetry at the QCP.…”

Section: B Chiral Xy Modelmentioning

confidence: 99%

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Four-loop critical exponents for the Gross-Neveu-Yukawa models

et al. 2017

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We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4 − ϵ dimensions and compute critical exponents for the GrossNeveu-Yukawa fixed points to order Oðϵ 4 Þ. Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in 2 þ 1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N ¼ 1=4 and N ¼ 1=2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

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Section: B Chiral Xy Modelmentioning

confidence: 99%

Section: B Chiral Xy Modelmentioning

confidence: 99%

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Four-loop critical exponents for the Gross-Neveu-Yukawa models

et al. 2017

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“…This adds a prime example to the general observation of fermion-induced symmetry enhancement in quantum critical Dirac systems. [11][12][13][14][15] Our results can be immediately applied to the triple point between the semimetallic and the O(3) Néel and U(1) Kekulé valence bond solid phases on the honeycomb lattice. The crucial ingredient here is the anticommuting nature of the corresponding Dirac mass terms, enabling us to combine them into a single order parameter that becomes a vector under O(5).…”

mentioning

confidence: 99%

Compatible orders and fermion-induced emergent symmetry in Dirac systems

Janssen¹,

Herbut²,

Scherer³

2018

Phys. Rev. B

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We study the quantum multicritical point in a (2+1)D Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with O(N1) and O(N2) symmetry, respectively. Using expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent O(N1 + N2) symmetry for arbitrary values of N1 and N2 and fermion flavor numbers N f , as long as the corresponding representation of the Clifford algebra exists. Small O(N )-breaking perturbations near the chiral O(N ) fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic O(N ) fixed point, which is stable only when N < 3. As a by-product, we obtain predictions for the critical behavior of the chiral O(N ) universality classes for arbitrary N and fermion flavor number N f . Implications for critical Weyl and Dirac systems in (3+1)D are also briefly discussed.Introduction. The interplay and competition of different ordering tendencies in many-body systems are the source of various exciting phenomena, including unconventional superconductivity, the nature of quantum spin liquids, and the physics of deconfined criticality. These notoriously challenging problems sometimes become theoretically accessible when an emergent higher symmetry can be found. The complex phase diagram of the high-T c superconductors, for instance, has been argued to be deducible from an emergent symmetry in which the O(3) Néel and U(1) superconducting order parameters are combined into a five-tuplet which turns out to be a vector under O(5).1 Numerical simulations of the deconfined critical point between the Néel and valence bond solid orders on the square lattice also find evidence for an emergent O(5) symmetry.2 The emergence of this symmetry can be made natural by postulating duality relations between the bosonic gauge theory describing the deconfined critical point and certain fermionic theories.3,4 Similarly, recent quantum Monte Carlo simulations of Dirac fermions in 2 + 1 dimensions find a direct and continuous transition between O(3) and Z 2 ordered phases with an emergent O(4) symmetry at criticality.

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“…There are multiple interesting directions for expanding our work, and a few of them are given below. While many QMC studies have been done for the Chiral Heisenberg universality class and now the Chiral Ising universality class as well, which consist of Dirac fermions acquiring mass by breaking SU p2q and Z 2 symmetries, respectively, there is still more need to establish the behavior for the Chiral XY universality class, where Dirac fermions acquire mass by breaking a U p1q symmetry [55]. There are models assumed to be in this class that can be simulated without sign problems, and they appear to be amenable to our new Hamiltonian fermion bag techniques.…”

Section: -Rachel Held Evansmentioning

confidence: 99%

Fermion Bag Approach to Lattice Hamiltonian Field Theories

Huffman

2018

EPJ Web Conf.

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Fermion Bag Approach for Hamiltonian Lattice Field TheoriesAbstract Understanding the critical behavior near quantum critical points for strongly correlated quantum many-body systems remains intractable for the vast majority of scenarios. Challenges involve determining if a quantum phase transition is first-or second-order, and finding the critical exponents for second-order phase transitions.Learning about where second-order phase transitions occur and determining their critical exponents is particularly interesting, because each new second-order phase transition defines a new quantum field theory.Quantum Monte Carlo (QMC) methods are one class of techniques that, when applicable, offer reliable ways to extract the nonperturbative physics near strongly coupled quantum critical points. However, there are two formidable bottlenecks to the applicability of QMC: (1) the sign problem and (2) algorithmic update inefficiencies. In this thesis, I overcome both these difficulties for a class of problems by extending the fermion bag approach recently developed by Shailesh Chandrasekharan to the Hamiltonian formalism and by demonstrating progress using the example of a specific quantum system known as the t-V model, which exhibits a transition from a semimetal to an insulator phase for a single flavor of four-component Dirac fermions.I adapt the fermion bag approach, which was originally developed in the context of Lagrangian lattice field theories, to be applicable within the Hamiltonian formalism, and demonstrate its success in two ways: first, through solutions to new sign iv problems, and second, through the development of new efficient QMC algorithms. In addressing the first point, I present a solution to the sign problem for the t-V model.While the t-V model is the simplest Gross-Neveu model of the chiral Ising universality class, the specter of the sign problem previously prevented its simulation with QMC for 30 years, and my solution initiated the first QMC studies for this model.The solution is then extended to many other Hamiltonian models within a class that involves fermions interacting with quantum spins. Some of these models contain an interesting quantum phase transition between a massless/semimetal phase to a massive/insulator phase in the so called Gross-Neveu universality class. Thus, the new solutions to the sign problem allow for the use of the QMC method to study these universality classes.The second point is addressed through the construction of a Hamiltonian fermion bag algorithm. The algorithm is then used to compute the critical exponents for the second-order phase transition in the t-V model. By pushing the calculations to significantly larger lattice sizes than previous recent computations (64 2 sites versus 24 2 sites), I am able to compute the critical exponents more reliably here compared to earlier work. I show that the inclusion of these larger lattices causes a significant shift in the values of the critical exponents that was not evident for the smaller lattices. This shift puts the critic...

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Fermion-induced quantum critical points

Cited by 124 publications

References 60 publications

Four-loop critical exponents for the Gross-Neveu-Yukawa models

Four-loop critical exponents for the Gross-Neveu-Yukawa models

Compatible orders and fermion-induced emergent symmetry in Dirac systems

Fermion Bag Approach to Lattice Hamiltonian Field Theories

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