Showing papers on "Explicit symmetry breaking published in 2019"

Interplay of dynamical and explicit chiral symmetry breaking effects on a quark

Abstract: The relative contributions of explicit and dynamical chiral symmetry breaking in QCD models of the quark-gap equation are studied in dependence of frequently employed Ans\"atze for the dressed interaction and quark-gluon vertex. The explicit symmetry breaking contributions are defined by a constituent-quark sigma term whereas the combined effects of explicit and dynamical symmetry breaking are described by a Euclidean constituent-mass solution. We extend this study of the gap equation to a quark-gluon vertex beyond the Abelian approximation complemented with numerical gluon- and ghost-dressing functions from lattice QCD. We find that the ratio of the sigma term over the Euclidean mass is largely independent of nonperturbative interaction and vertex models for current-quark masses, ${m}_{u,d}(\ensuremath{\mu})\ensuremath{\le}m(\ensuremath{\mu})\ensuremath{\le}{m}_{b}(\ensuremath{\mu})$, and equal contributions of explicit and dynamical chiral symmetry breaking occur at $m(\ensuremath{\mu})\ensuremath{\approx}400\text{ }\text{ }\mathrm{MeV}$. For massive solutions of the gap equation with lattice propagators this value decreases to about 220 MeV.

Chiral Symmetry Breaking on the Lattice

Abstract: We review important aspects of QCD in the continuum and on the lattice and take a look at the fate of its symmetries with an emphasis on chiral symmetry breaking on the lattice.

Unidirectional Magnon-Driven Domain Wall Motion Due to the Interfacial Dzyaloshinskii-Moriya Interaction.

Abstract: We demonstrate a unidirectional motion of a quasiparticle without explicit symmetry breaking along the space-time coordinate of the particle motion. This counterintuitive behavior originates from a combined action of two intrinsic asymmetries in the other two directions. We realize this idea with the magnon-driven motion of a magnetic domain wall in thin films with interfacial asymmetry. Contrary to previous studies, the domain wall moves along the same direction regardless of the magnon-flow direction. Our general symmetry analysis and numerical simulation reveal that the odd order contributions from the interfacial asymmetry is unidirectional, which is dominant over bidirectional contributions in the realistic regime. We develop a simple analytic theory on the unidirectional motion, which provides an insightful description of this counterintuitive phenomenon.

Folding approach to topological order enriched by mirror symmetry

Abstract: We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be conveniently studied through previously known tools: (i) it maps the nonlocal mirror symmetry to an onsite $\mathbb{Z}_2$ layer-exchange symmetry after folding the SET along the mirror axis, so that we can gauge the symmetry; (ii) it maps all mirror SET information into the boundary properties of the folded system, so that they can be studied by the anyon condensation theory---a general theory for studying gapped boundaries of topological orders; and (iii) it makes the mirror anomalies explicitly exposed in the boundary properties, i.e., strictly 2D SETs and those that can only live on the surface of a 3D system can be easily distinguished through the folding approach. With the folding approach, we derive a set of physical constraints on data that describes mirror SET, namely mirror permutation and mirror symmetry fractionalization on the anyon excitations in the topological order. We conjecture that these constraints may be complete, in the sense that all solutions are realizable in physical systems. Several examples are discussed to justify this. Previously known general results on the classification and anomalies are also reproduced through our approach.

Persistence of stationary motion under explicit symmetry breaking perturbation

Abstract: Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed in a way that the perturbation preserves only some symmetries of the original system. We give a geometric approach to study this phenomenon in the setting of Hamiltonian systems. We provide a method for determining the equilibria and relative equilibria that persist after a symmetry breaking perturbation. In particular a lower bound for the number of each is found, in terms of an equivariant Lyusternik-Schnirelmann category of the group orbit.

Spin separation in the half-filled fractional topological insulator

Abstract: All topological insulators observed so far are the lattice analogs of the integer quantum Hall states with time-reversal symmetry, composed of two decoupled copies of the Chern insulator with opposite chiralities for different spins. The fractional topological insulator (FTI) has been similarly envisioned as being composed of two decoupled copies of the fractional Chern insulator (FCI), which is in turn the lattice analog of the fractional quantum Hall state (FQHS). An important question is if such a vision can be realized for the Coulomb interaction, whose strength is irrespective of spin. To address this question, we investigate the effects of the interspin correlation in the spin-holomorphic Landau levels, where electrons with one spin reside in the usual holomorphic lowest Landau level, while those with the other in the antiholomorphic counterpart. By performing exact diagonalization of the Coulomb interaction Hamiltonian in the spin-holomorphic Landau levels, here, we show that no fractionally filled states in the spin-holomorphic Landau levels can occur as two decoupled copies of the FQHS, suggesting that no FTIs can occur as those of the FCI in the lattice either. Fractionally filled states in this system are generally compressible except at half filling, where a transport gap develops with spontaneous breaking of the space rotational symmetry in the thermodynamic limit, leading to the spatial separation of different spins, i.e., spin separation. It is predicted that there is a novel bulk-edge correspondence at half filling, representing the hallmark of the half-filled spin-separated FTI.

Chiral Nonsymmetric Interaction in Strong Coupled QCD

Abstract: Chiral symmetry in massless QCD is believed to be broken spontaneously. We discuss a possibility that the chiral symmetry is explicitly broken by QCD monopoles which appear only in strong coupled QCD. Namely, the monopole quark interaction explicitly breaks the chiral symmetry ( SU$_A(2)\times $U$_A$(1) ) just like bare quark mass terms. We show that the strength of the interaction is roughly $10$ times smaller than standard strong interactions. We describe it as an effective interaction $g'\bar{q}q\Phi^{\dagger}\Phi$ with the monopole field $\Phi$ and $g'$ being of the order of $(10\rm \,GeV)^{-1}$ or less. It produces small constituent quark masses less than $1$MeV when the monopoles condense ( $\langle\Phi\rangle eq 0 $ ). We examine to what extent such a weak but explicit symmetry breaking interaction is allowed. In particular, examining Gell-Mann-Oakes-Renner relation we find that the presence of such a small symmetry breaking term is still allowed within the present accuracy of lattice gauge simulations. We predict some phenomenological effects caused by the chiral nonsymmetric monopole quark interaction. Quark confinement and chiral condensate ( $\langle\bar{q}q\rangle eq 0$ ) arise simultaneously. The condensate $\langle\bar{q}q\rangle$ caused by the monopoles is proportional to monopole density and is estimated such that $(-\langle\bar{q}q\rangle)^{1/3}\sim 160$MeV. The weak monopole quark interaction leads to the small decay width of an observable monopole to hadrons.