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

He, Yuan-Yao; Wu, Han‐Qing; You, Yi-Zhuang; Xu, Cenke; Meng, Zi Yang; Lu, Zhong-Yi

doi:10.1103/physrevb.94.241111

Cited by 29 publications

(33 citation statements)

References 32 publications

(30 reference statements)

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“…In this work we explore a different mechanism of fermion mass generation where fermions acquire their mass through four-fermion condensates, while fermion bilinear condensates vanish. This alternate mechanism has been the focus of many recent studies in 3D lattice models [1][2][3][4][5][6]. Here we explore if these results extend to 4D.…”

Section: Introductionmentioning

confidence: 77%

Fermion masses through four-fermion condensates

Ayyar

Chandrasekharan

2016

J. High Energ. Phys.

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Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.

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Section: Introductionmentioning

confidence: 77%

Fermion masses through four-fermion condensates

Ayyar

Chandrasekharan

2016

J. High Energ. Phys.

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“…It is obvious that only when θ(φ i j ) = 0 or π, B z,b (i, j) will be diagonalized by an auxiliary field independent unitary transformation, and then the aforementioned fast update scheme applies. There are many known models belong to this case, such as model with Heisenberg type interaction [57][58][59], models with Z 2 (bosonic) gauge field coupled to fermionic matter [18,19,60,61], etc. Novel physics has been found in these models, for example in Ref.…”

Section: Difficulties Of the Qmc Simulationmentioning

confidence: 99%

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Zhang

et al. 2019

Phys. Rev. X

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101

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The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact U(1) lattice gauge theory coupled to fermionic matter in (2 + 1)D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are incarnation of an exotic states of matter, i.e. the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, N f = 4, our data suggests a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

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“…These models are similar to the Thirring model considered in the present work. Numerical simulations with staggered fermions, the fermion bag method, hybrid Monte Carlo and quantum Monte Carlo revealed actually an interesting phase structure [37][38][39][40]: The systems exhibit a continuous quantum phase transition from a weakly coupled massless phase (a gapless Dirac semimetal) to a massive (fully gapped Mott insulator) phase without condensing any fermion bilinear operator. It could very well be that a similar mechanism is at work in the Thirring models, although a bilinear condensate is not forbidden by symmetry arguments as it is in the SU(4)-invariant models.…”

Section: Susceptibilitymentioning

confidence: 99%

Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions

2019

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The Thirring model is an interacting fermion theory with current-current interaction. The model in 1 + 2 dimensions has applications in condensed-matter physics to describe the electronic excitations of Dirac materials. Earlier investigations with Schwinger-Dyson equations, the functional renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible) flavors N c exists, below which chiral symmetry can be broken spontaneously. Values for N c found in the literature vary between 2 and 7. Recent lattice studies with chirally invariant SLAC fermions have indicated that chiral symmetry is unbroken for all integer flavor numbers [1,2]. An independent simulation based on domain wall fermions seems to favor a critical flavornumber that satisfies 1 < N c < 2 [3]. However, in the latter simulations difficulties in reaching the massless limit in the broken phase (at strong coupling and after the Ls → ∞ limit has been taken) are encountered. To find an accurate value N c we study the Thirring model (by using an analytic continuation of the parity even theory to arbitrary real N ) for N between 0.5 and 1.1. We investigate the chiral condensate, the spectral density of the Dirac operator, the spectrum of (would-be) Goldstone bosons and the variation of the filling-factor and conclude that the critical flavor number is N c = 0.80(4). Thus we see no chiral symmetry breaking in all Thirring models with 1 or more flavors of (4-component) fermions. Besides the transition to the unphysical lattice artifact phase we find strong evidence for a hitherto unknown phase transition that exists for N > N c and should answer the question of where to construct a continuum limit.

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

Cited by 29 publications

References 32 publications

Fermion masses through four-fermion condensates

Fermion masses through four-fermion condensates

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions

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