Quantum diffusion of massive Dirac fermions induced by symmetry breaking

Abstract We investigate a model of interacting Dirac fermions in 2 + 1 dimensions with M flavors and N colors having the U(M)×SU(N ) symmetry. In the large-N limit, we find that the U(M) symmetry is spontaneously broken in a variety of ways. In the vacuum, when the parity-breaking flavor-singlet mass is varied, the ground state undergoes a sequence of M first-order phase transitions, experiencing M + 1 phases characterized by symmetry breaking U(M)→U(M − k)×U(k) with k ∈ {0, 1, 2, · · · , M}, bearing a close resemblance to the vacuum structure of three-dimensional QCD. At finite temperature and chemical potential, a rich phase diagram with first and second-order phase transitions and tricritical points is observed. Also exotic phases with spontaneous symmetry breaking of the form as U(3)→U(1)3, U(4)→U(2)×U(1)2, and U(5)→U(2)2×U(1) exist. For a large flavor-singlet mass, the increase of the chemical potential μ brings about M consecutive first-order transitions that separate the low-μ phase diagram with vanishing fermion density from the high-μ region with a high fermion density.

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Gross–Neveu–Yukawa and Gross–Neveu models

Quantum Field Theory and Critical Phenomena ◽

10.1093/oso/9780198834625.003.0020 ◽

2021 ◽

pp. 489-506

Author(s):

Jean Zinn-Justin

Keyword(s):

Phase Transition ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Particle Physics ◽

Continuous Phase ◽

Two Dimensions ◽

Fermion Mass ◽

Dirac Fermions ◽

Mass Generation ◽

Four Dimensions

In this chapter, a model is considered that can be defined in continuous dimensions, the Gross– Neveu–Yukawa (GNY) model, which involves N Dirac fermions and one scalar field. The model has a continuous U(N) symmetry, and a discrete symmetry, which prevents the addition of a fermion mass term to the action. For a specific value of a coefficient of the action, the model undergoes a continuous phase transition. The broken phase illustrates a mechanism of spontaneous symmetry breaking, leading to spontaneous fermion mass generation like in the Standard Model (SM) of particle physics. In four dimensions, the GNY can be considered as a toy model to represent the interactions between the top quark and the Higgs boson, the heaviest particles of the SM of fundamental interactions, when the gauge fields are omitted. The model is renormalizable in four dimensions and its renormalization group (RG) properties can be studied in d = 4 and d = 4 − ϵ dimensions. A model of self-interacting fermions with the same symmetries and fermion content, the Gross–Neveu (GN) model, has been widely studied. In perturbation theory, for d > 2, it describes only a phase with massless fermions but, in d = 2 + ϵ dimensions, the RG indicates that, at a critical value of the coupling constant, the model experiences a phase transition. In two dimensions, it is renormalizable and exhibits the phenomenon of asymptotic freedom. The massless phase becomes infrared unstable and there is strong evidence that the spectrum corresponds to spontaneous symmetry breaking and fermion mass generation.

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Superconductivity, correlated insulators, and Wess–Zumino–Witten terms in twisted bilayer graphene

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2014691117 ◽

2020 ◽

Vol 117 (47) ◽

pp. 29543-29554

Author(s):

Maine Christos ◽

Subir Sachdev ◽

Mathias S. Scheurer

Keyword(s):

High Temperature ◽

Low Temperature ◽

Band Structure ◽

Symmetry Breaking ◽

Bilayer Graphene ◽

Flavor Symmetry ◽

Dirac Fermions ◽

Parent State ◽

Comprehensive Listing ◽

Twisted Bilayer Graphene

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess–Zumino–Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a “mechanism” for superconductivity. We present a comprehensive listing of plausible low-temperature orders and the parent flavor symmetry-breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis.

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Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

1989 ◽

Vol 47 ◽

pp. 480-481

Author(s):

D.J. Eaglesham

Keyword(s):

Symmetry Breaking ◽

Point Group ◽

X Ray Diffraction ◽

Multiple Diffraction ◽

Space Groups ◽

Atomic Displacements ◽

Small Probe ◽

Phase Sensitive ◽

Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

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Centrosome Aurora A gradient ensures single polarity axis in C. elegans embryos

Biochemical Society Transactions ◽

10.1042/bst20200298 ◽

2020 ◽

Vol 48 (3) ◽

pp. 1243-1253 ◽

Cited By ~ 1

Author(s):

Sukriti Kapoor ◽

Sachin Kotak

Keyword(s):

Symmetry Breaking ◽

Cell Fate ◽

Cell Cortex ◽

Axis Formation ◽

Aurora A Kinase ◽

Aurora A ◽

C Elegans ◽

Cell Embryo ◽

Polarity Establishment

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.

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