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Register a new userChiral symmetry breaking in lattice brane QED model
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We propose a novel lattice calculation of spontaneous chiral symmetry breaking in QED model with 2+1 dimensional fermion brane. Considering the relativistic action with gauge symmetry we rigorously carry out path integral in Monte-Carlo simulation with Fermi-velocity relevant to effective coupling constant. We numerically show the evidence of spontaneous chiral symmetry breaking in strong coupling region with chiral condensate, low-lying mode distribution and Nambu-Goldstone boson spectrum in bare Fermi-velocty $v=0.1$. This is a feasible study to investigate the phase structure of Graphene.
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We propose a novel approach to the Graphene system using a local field theory of 4 dimensional QED model coupled to 2+1 dimensional Dirac fermions, whose velocity is much smaller than the speed of light. Performing hybrid Monte Carlo simulations of this model on the lattice, we compute the chiral condensate and its susceptibility with different coupling constant, velocity parameter and flavor number. We find that the chiral symmetry is dynamically broken in the small velocity regime and obtain a qualitatively consistent behavior with the prediction from Schwinger-Dyson equations.
We study perturbations that break gauge symmetries in lattice gauge theories. As a paradigmatic model, we consider the three-dimensional Abelian-Higgs (AH) model with an N-component scalar field and a noncompact gauge field, which is invariant under U(1) gauge and SU(N) transformations. We consider gauge-symmetry breaking perturbations that are quadratic in the gauge field, such as a photon mass term, and determine their effect on the critical behavior of the gauge-invariant model, focusing mainly on the continuous transitions associated with the charged fixed point of the AH field theory. We discuss their relevance and compute the (gauge-dependent) exponents that parametrize the departure from the critical behavior (continuum limit) of the gauge-invariant model. We also address the critical behavior of lattice AH models with broken gauge symmetry, showing an effective enlargement of the global symmetry, from U(N) to O(2N), which reflects a peculiar cyclic renormalization-group flow in the space of the lattice AH parameters and of the photon mass.
We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various confinement indicators, such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $lambda_n$ such as $lambda_n^{N_t-1}$, which behaves as a reduction factor for small $lambda_n$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities,while they are essential for chiral symmetry breaking. These relations indicate no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, respectively, and find the similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry.
We perform a lattice study, in the quenched approximation, of dynamical mass generation in a system of relativistic (Dirac) fermions, coupled to an Abelian gauge field in (2+1)-dimensions, in the presence of an external (constant) magnetic field, perpendicular to the spatial planes. It is shown that a strong magnetic field catalyzes chiral symmetry breaking, in agreement with results in the continuum. The r^ole of the higher-Landau poles in inducing a critical temperature above which the phenomenon disappears is pointed out. We also discuss the implications of this model on the opening of a gap in doped antiferromagnetic superconductors.
Using lattice QCD we study the spectrum of low-lying fermion eigenmodes. According to the Banks-Casher relation, accumulation of the low-mode is responsible for the spontaneous breaking of chiral symmetry in the QCD vacuum. On the lattice we use the overlap fermion formulation that preserves exact chiral symmetry. This is essential for the study of low-lying eigenmode distributions. Through a detailed comparison with the expectations from chiral perturbation theory beyond the leading order, we confirm the senario of the spontaneous symmetry breaking and determine some of the low energy constants. We also discuss on other related physical quantities, which can be studied on the lattice with exact chiral symmetry.
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