Massive fermions without fermion bilinear condensates

Ayyar, Venkitesh; Chandrasekharan, Shailesh

doi:10.1103/physrevd.91.065035

Cited by 65 publications

(84 citation statements)

References 56 publications

(88 reference statements)

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“…The quantum critical point at V c /t = 2.00 ± 0.05 separate the gapless Dirac semimetal from the featureless Mott insulator. Such new mechanism of mass generation without fermion bilinear condensation is consistent with previous studies from the lattice QCD community [21][22][23]. More interestingly, in our investigations, the excitation gaps and an exhaustive exclusion of symmetry breaking are for the first time being directly accessed and a large anomalous dimension η at the DSM-FMI transition is revealed.…”

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confidence: 76%

“…This new mechanism of mass generation was tested and confirmed numerically by both condensed matter [20] and lattice QCD [21][22][23] physicists, using quantum Monte Carlo simulation methods. These works provide evidence that the massless Dirac fermion phase and the massive quantum phase without any fermion mass condensation are connected by a single continuous quantum phase transition.…”

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confidence: 99%

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Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

You

et al. 2016

Phys. Rev. B

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We study a lattice model of interacting Dirac fermions in (2 + 1) dimension space-time with an SU(4) symmetry. While increasing interaction strength, this model undergoes a continuous quantum phase transition from the weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progresses in lattice QCD community. Introduction. In the Standard Model of particle physics, all the matter fields, quarks and leptons, acquire their mass from "spontaneous symmetry breaking", or equivalently the condensation of the Higgs field [1-3]. The Higgs field couples to the bilinear mass operator of the Dirac fermion matter fields (except for the neutrinos), and hence the matters acquire a mass in the condensate. In the context of correlated electron systems, mass generation (or gap opening) due to interaction is also often a consequence of spontaneous symmetry breaking and the development of certain long-range order. For example, in a superconductor the Cooper pairs condense, which spontaneously breaks the U (1) charge symmetry of the electrons, and as a result the electrons acquire a mass gap at the Fermi surface. So, consensus has that, in strongly interacting fermionic systems (either in condensed matter or high energy physics), mass (or gap) generation is usually related to spontaneous symmetry breaking and the condensation of a fermion bilinear operator [4].

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confidence: 76%

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confidence: 99%

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

You

et al. 2016

Phys. Rev. B

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“…At weak couplings, since the fourfermion coupling U is irrelevant, we expect massless fermions. At strong couplings, it can be argued using the fermion bag approach [13] that all two point correlations must decay exponentially. Hence, we expect massive fermions without any fermion bilinear condensates (PMS phase).…”

Section: Computational Approachmentioning

confidence: 99%

Search for a continuum limit of the PMS phase

Ayyar¹

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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Previous studies of a simple four-fermion model with staggered fermions in 3D have shown the existence of an exotic quantum critical point, where one may be able to define a continuum limit of the Paramagnetic Strong Phase (or the PMS phase). We believe the existence of the critical point suggests a new mechanism for generating fermion masses. In this work we begin the search for this quantum critical point in 4D by extending the 3D model to 4D. Unlike in 3D, now we do find evidence for an intermediate spontaneously broken phase (FM phase) and are able compute the phase boundaries accurately. In terms of the bare coupling, the width of the intermediate region appears to be quite small. 34th annual International Symposium on Lattice Field Theory

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“…The same field theory Lagrangian must be applicable to the interaction driven mass gap at the boundary of 16 copies of the 3 He-B phase. The only difference is that, at the 2d boundary of 3 He-B a fermion bilinear mass term is prohibited by time-reversal symmetry only, while in our 2d lattice model crystalline symmetry is required to prevent fermion bilinear mass terms.We also note that a similar phase transition between gapless Dirac fermions and a symmetric gapped phase was recently also studied in high energy physics communities [19]. Now let us consider the case with finite λ.…”

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confidence: 99%

“…We also note that a similar phase transition between gapless Dirac fermions and a symmetric gapped phase was recently also studied in high energy physics communities [19]. Now let us consider the case with finite λ.…”

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Exotic quantum phase transitions of strongly interacting topological insulators

Slagle

You

2015

Phys. Rev. B

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Using determinant quantum Monte Carlo (d-QMC) simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin S z conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single particle excitations remain gapped, while spin and charge gap both close. We argue that the first quantum phase transition is related to the Z16 classification of the topological superconductor 3 He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O(4) nonlinear sigma model field theory with a Θ-term.IntroductionThe interplay between topology and interactions can lead to very rich new physics. For bosonic systems, it is understood that strong interactions can lead to many symmetry protected topological (SPT) phases [1,2] that are fundamentally different from the standard Mott insulator and superfluid phases. In addition to producing various topological orders, for fermionic systems strong interactions can also reduce the classification of free fermion topological insulators and superconductors [3][4][5][6][7][8][9][10][11]. That is, interactions can drive free fermion topological superconductors to a trivial phase; namely the edge states of the free fermion topological superconductor can be gapped out without degeneracy by a symmetry preserving short range interactions without going through a bulk quantum phase transition. The most famous example is the 3 He-B topological superconductor protected by time-reversal symmetry, whose boundary is described by a (2 + 1)d Majorana fermion χ with theHe-B has a Z classification; therefore for arbitrary copies of 3 He-B, its boundary remains gapless as long as time-reversal symmetry is preserved [12][13][14]. In other words any fermion-bilinear mass term χ a σ y χ b at the boundary would break the time-reversal symmetry. However, once interactions are turned on, the classification of 3 He-B is reduced to Z 16 ; i.e., with 16 copies of 3 He-B, its boundary can be gapped out by interactions while preserving the time-reversal symmetry [9,10]. In other words, the boundary is fully gapped by interactions with χ a σ y χ b = 0, for a, b = 1 · · · 16.Although the classification of interacting 3 He-B has been understood, the following question remains: if the interactions are tuned continuously, can there be a direct second order quantum phase transition between the weakly interacting gapless boundary and the strongly interacting fully gapped nondegenerate boundary state? Even if such a second order phase transition exists, its field theory description is unknown because the standard field ...

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Massive fermions without fermion bilinear condensates

Cited by 65 publications

References 56 publications

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

Search for a continuum limit of the PMS phase

Exotic quantum phase transitions of strongly interacting topological insulators

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