Broken Discrete Symmetry Research Articles

Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries

We show how decimated Gibbs measures having unbroken continuous symmetry due to the Mermin–Wagner theorem, despite their discrete equivalents exhibiting phase transition, can still become non-Gibbsian. The mechanism rests on the occurrence of a spin-flop transition with a broken discrete symmetry, once the model is constrained by the decimated spins in a suitably chosen “bad” configuration.

Engineering Domain Wall Electronic States in Strongly Correlated van der Waals Material of 1T-TaS2.

Although a few physical methods were demonstrated for domain wall engineering in various electronic or ferroic materials with broken discrete symmetries, the direct control over the electronic properties of individual domain walls has been extremely limited. Here, we introduce a chemical method to tune the electronic property of domain walls in 1T tantalum disulfide. By using scanning tunneling microscopy and spectroscopy techniques, we find that indium adatoms on 1T-TaS2 have distinct behaviors on the domains with different bulk terminations. Moreover, the adatoms form their own chains along the edges of neighboring domains. The density functional theory calculations reveal a 1D Mott insulating state on a modified domain wall, resulting from the degenerated spin-polarized bands with electron doping from adsorbates and charge transfer from neighboring domains. This work suggests that chemical decoration by adsorbates can be widely used to tune local electronic states of domain walls and various 2D materials.

Evidence for nematic superconductivity of topological surface states in PbTaSe2

Spontaneous symmetry breaking has been a paradigm to describe the phase transitions in condensed matter physics. In addition to the continuous electromagnetic gauge symmetry, an unconventional superconductor can break discrete symmetries simultaneously, such as time reversal and lattice rotational symmetry. In this work we report a characteristic in-plane 2-fold behaviour of the resistive upper critical field and point-contact spectra on the superconducting semimetal PbTaSe2 with topological nodal-rings, despite its hexagonal lattice symmetry (or D3h in bulk while C3v on surface, to be precise). The 2-fold behaviour persists up to its surface upper critical field Hc2R even though bulk superconductivity has been suppressed at its bulk upper critical field Hc2HC≪Hc2R, signaling its probable surface-only electronic nematicity. In addition, we do not observe any lattice rotational symmetry breaking signal from field-angle-dependent specific heat within the resolution. It is worth noting that such surface-only electronic nematicity is in sharp contrast to the observation in the topological superconductor candidate, CuxBi2Se3, where the nematicity occurs in various bulk measurements. In combination with theory, superconducting nematicity is likely to emerge from the topological surface states of PbTaSe2, rather than the proximity effect. The issue of time reversal symmetry breaking is also addressed. Thus, our results on PbTaSe2 shed new light on possible routes to realize nematic superconductivity with nontrivial topology.

Effects of biases in domain wall network evolution. II. Quantitative analysis

Domain walls form at phase transitions which break discrete symmetries. In a cosmological context they often overclose the universe (contrary to observational evidence), although one may prevent this by introducing biases or forcing anisotropic evolution of the walls. In a previous work [Correia {\it et al.}, Phys.Rev.D90, 023521 (2014)] we numerically studied the evolution of various types of biased domain wall networks in the early universe, confirming that anisotropic networks ultimately reach scaling while those with a biased potential or biased initial conditions decay. We also found that the analytic decay law obtained by Hindmarsh was in good agreement with simulations of biased potentials, but not of biased initial conditions, and suggested that the difference was related to the Gaussian approximation underlying the analytic law. Here we extend our previous work in several ways. For the cases of biased potential and biased initial conditions we study in detail the field distributions in the simulations, confirming that the validity (or not) of the Gaussian approximation is the key difference between the two cases. For anisotropic walls we carry out a more extensive set of numerical simulations and compare them to the canonical velocity-dependent one-scale model for domain walls, finding that the model accurately predicts the linear scaling regime after isotropization. Overall, our analysis provides a quantitative description of the cosmological evolution of these networks.

Primordial black hole and wormhole formation by domain walls

In theories with a broken discrete symmetry, Hubble sized spherical domain walls may spontaneously nucleate during inflation. These objects are subsequently stretched by the inflationary expansion, resulting in a broad distribution of sizes. The fate of the walls after inflation depends on their radius. Walls smaller than a critical radius fall within the cosmological horizon early on and collapse due to their own tension, forming ordinary black holes. But if a wall is large enough, its repulsive gravitational field becomes dominant much before the wall can fall within the cosmological horizon. In this ``supercritical'' case, a wormhole throat develops, connecting the ambient exterior FRW universe with an interior baby universe, where the exponential growth of the wall radius takes place. The wormhole pinches off in a time-scale comparable to its light-crossing time, and black holes are formed at its two mouths. As discussed in previous work, the resulting black hole population has a wide distribution of masses and can have significant astrophysical effects. The mechanism of black hole formation has been previously studied for a dust-dominated universe. Here we investigate the case of a radiation-dominated universe, which is more relevant cosmologically, by using numerical simulations in order to find the initial mass of a black hole as a function of the wall size at the end of inflation. For large supercritical domain walls, this mass nearly saturates the upper bound according to which the black hole cannot be larger than the cosmological horizon. We also find that the subsequent accretion of radiation satisfies a scaling relation, resulting in a mass increase by about a factor of 2.

Magnetization plateaus of an easy-axis kagome antiferromagnet with extended interactions

We investigate the properties in finite magnetic field of an extended anisotropic XXZ spin-1/2 model on the Kagome lattice, originally introduced by Balents, Fisher, and Girvin [Phys. Rev. B, 65, 224412 (2002)]. The magnetization curve displays plateaus at magnetization m=1/6 and 1/3 when the anisotropy is large. Using low-energy effective constrained models (quantum loop and quantum dimer models), we discuss the nature of the plateau phases, found to be crystals that break discrete rotation and/or translation symmetries. Large-scale quantum Monte-Carlo simulations were carried out in particular for the m=1/6 plateau. We first map out the phase diagram of the effective quantum loop model with an additional loop-loop interaction to find stripe order around the point relevant for the original model as well as a topological Z2 spin liquid. The existence of a stripe crystalline phase is further evidenced by measuring both standard structure factor and entanglement entropy of the original microscopic model.

2HDM with extra U(1)H gauge symmetry

General two Higgs doublet models suffer excessive flavor changing neutral currents (FCNC) mediated by the neutral Higgs. A way to avoid this problem is to impose a discrete symmetry of type Z2. However, it is known that spontaneously broken discrete symmetries can lead to the problem of domain walls, as indeed happens in the case of the 2HDM. In this work we review the consequences of the substitution of the Z2 symmetry by a new U(1)H gauge symmetry, associated with the Higgs flavors, in which H1 and H2 have different charges of the U(1)H group.

Thermodynamic chemical energy transfer mechanisms of non-equilibrium, quasi-equilibrium, and equilibrium chemical reactions

Chemical energy transfer mechanisms at finite temperature are explored by a chemical energy transfer theory which is capable of investigating various chemical mechanisms of non-equilibrium, quasi-equilibrium, and equilibrium. Gibbs energy fluxes are obtained as a function of chemical potential, time, and displacement. Diffusion, convection, internal convection, and internal equilibrium chemical energy fluxes are demonstrated. The theory reveals that there are chemical energy flux gaps and broken discrete symmetries at the activation chemical potential, time, and displacement. The statistical, thermodynamic theory is the unification of diffusion and internal convection chemical reactions which reduces to the non-equilibrium generalization beyond the quasi-equilibrium theories of migration and diffusion processes. The relationship between kinetic theories of chemical and electrochemical reactions is also explored. The theory is applied to explore non-equilibrium chemical reactions as an illustration. Three variable separation constants indicate particle number constants and play key roles in describing the distinct chemical reaction mechanisms. The kinetics of chemical energy transfer accounts for the four control mechanisms of chemical reactions such as activation, concentration, transition, and film chemical reactions.

Heat transfer theory for thermal non-equilibrium, quasi-equilibrium, and equilibrium

Heat transfer is one of the fundamental and veiled energy transfer processes. The complex characteristics of heat transfer in a thermal process are far from being understood entirely. We here propose a statistical thermodynamic transport theory which is applicable to the heat transfer mechanisms for non-equilibrium, quasi-equilibrium, and equilibrium to overcome limits on the heat diffusion equation. The heat transfer theory adopts a postulate that temperature, time, and displacement are independent and orthogonal variables in extended phase spaces. The solutions of the heat transfer theory are obtained for thermal non-equilibrium, quasi-equilibrium, and equilibrium and the heat fluxes are expressed as the functions of temperature, time, and displacement. The heat transfer theory demonstrates that there are heat flux gaps and broken discrete symmetries at the activation temperature, time, and displacement. The theory is consistent with statistical thermodynamics. The kinetic theory is the unification of conduction and internal convection heat transfer, a non-equilibrium generalization beyond quasi-equilibrium theories for isothermal and isentropic processes, and the integration of internal equilibrium and internal non-equilibrium.

Broken discrete symmetries in a frustrated honeycomb antiferromagnet

We study the magnetic phase diagram of the $J_1$--$J_2$ Heisenberg antiferromagnet on a honeycomb lattice at the strongly frustrated point $J_2/J_1=1/2$ using large-scale Monte Carlo simulations. At low temperatures we find three different field regimes, each characterized by different broken discrete symmetries. In low magnetic fields up to $h_{c1}/J_1\approx 2.9$ the $Z_3$ rotational lattice symmetry is spontaneously broken while a 1/2-magnetization plateau is stabilized around $h_{c2}/J_1=4$. The collinear plateau state and the coplanar state in higher fields break the $Z_4$ translational symmetry and correspond to triple-$q$ magnetic structures. The intermediate phase $h_{c1}<h<h_{c2}$ has an interesting symmetry structure, breaking simultaneously the $Z_3$ and $Z_4$ symmetries. At much lower temperatures the spatial broken discrete symmetries coexist with the quasi long-range order of the transverse spin components.

Statistical Thermodynamic Theory for Non-Equilibrium, Quasi-Equilibrium, and Equilibrium Electrochemical Reactions

An electrochemical reaction as a branch of chemical reactions is one of the fundamental phenomena, but exact electrochemical reaction mechanisms have been unknown. We here propose a statistical thermodynamic theory for electrochemical reactions, which is vital to investigate electrochemical reactions for non-equilibrium, quasi-equilibrium, and equilibrium. The theory utilizes a postulate that electric potential, time, and space are independent and orthogonal variables in extended phase spaces. It is an internal Gibbs energy transport theory for electrochemical reactions leading to the unification of non-equilibrium and equilibrium reactions, a non-equilibrium generalization beyond quasi-equilibrium theories for migration and diffusion, and the integration of diffusion and convection mechanisms. It predicts that there are current density gaps and broken discrete symmetries at the activation potential, time, and displacement. It provides the Nernst equation, the rate equation, and the spatial cross section of electrochemical reactions. The electrochemical theory demonstrates relationships among electrochemical reactions, thermodynamics, and statistical physics.

Fluctuation relations for equilibrium states with broken discrete symmetries

Relationships are obtained expressing the breaking of spin-reversal symmetry by an external magnetic field in Gibbsian canonical equilibrium states of spin systems under specific assumptions. These relationships include an exact fluctuation relation for the probability distribution of the magnetization, as well as a relation between the standard thermodynamic entropy, an associated spin-reversed entropy or coentropy, and the product of the average magnetization with the external field, as a non-negative Kullback–Leibler divergence. These symmetry relations are applied to the model of noninteracting spins, the 1D and 2D Ising models, and the Curie–Weiss model, all in an external magnetic field. The results are drawn by analogy with similar relations obtained in the context of nonequilibrium physics.

Critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals

We compute the transition temperature ${T}_{c}$ and the Ginzburg temperature ${T}_{\mathrm{G}}$ above ${T}_{c}$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for ${T}_{c}$ and ${T}_{\mathrm{G}}$ as a function of the nonthermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between ${T}_{c}$ and ${T}_{\mathrm{G}}$ occupies a sizable part of the phase diagram.

INFORMATION AND PARTICLE PHYSICS

Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalization invariance and positivity. Those measures are then used to motivate generalized Lagrangians meant to probe shorter distance physics within the maximum uncertainty framework. The modified evolution equations that follow are necessarily nonlinear and simultaneously violate Lorentz invariance, supporting previous heuristic arguments linking quantum nonlinearity with Lorentz violation. The nonlinear equations also break discrete symmetries. We discuss the implications of our results for physics in the neutrino sector and cosmology.

Renormalization group for phases with broken discrete symmetry near quantum critical points

We extend the Hertz--Millis theory of quantum phase transitions in itinerant electron systems to phases with broken discrete symmetry. By using a set of coupled flow equations derived within the functional renormalization group framework, we compute the second order phase transition line ${T}_{c}(\ensuremath{\delta})$, where $\ensuremath{\delta}$ is a nonthermal control parameter, near a quantum critical point. We analyze the interplay and relative importance of quantum and classical fluctuations at different energy scales, and we compare the Ginzburg temperature ${T}_{G}$ to the transition temperature ${T}_{c}$, the latter being associated with a non-Gaussian fixed point.

Origin of artificial electrodynamics in three-dimensional bosonic models

Several simple models of strongly correlated bosons on three-dimensional lattices have been shown to possess exotic fractionalized Mott insulating phases with a gapless ``photon'' excitation. In this paper we show how to view the physics of this ``Coulomb'' state in terms of the excitations of proximate superfluid. We argue for the presence of ordered vortex cores with a broken discrete symmetry in the nearby superfluid phase and that proliferating these degenerate but distinct vortices with equal amplitudes produces the Coulomb phase. This provides a simple physical description of the origin of the exotic excitations of the Coulomb state. The physical picture is formalized by means of a dual description of three-dimensional bosonic systems in terms of fluctuating quantum mechanical vortex loops. Such a dual formulation is extensively developed. It is shown how the Coulomb phase (as well as various other familiar phases) of three-dimensional bosonic systems may be described in this vortex loop theory. For bosons at half-filling and the closely related system of spin-$1∕2$ quantum magnets on a cubic lattice, fractionalized phases as well as bond- or ``box''-ordered states are possible. The latter are analyzed by an extension of techniques previously developed in two spatial dimensions. The relation between these ``confining'' phases with broken translational symmetry and the fractionalized Coulomb phase is exposed.

Cosmology and broken discrete symmetry

It is argued that under various circumstances spontaneously broken discrete symmetry, which is commonly thought to lead to grave cosmological problems, need not do so. A particularly interesting example is the two-doublet version of the standard model. This extended model avoids unacceptable flavor-changing neutral currents in a natural way only if an appropriate discrete symmetry is postulated. Here it is shown that this discrete symmetry is anomalous. As a result, when it is spontaneously broken it does not produce stable domain walls (which would be problematic for cosmology). Instead an interesting cosmological scenario results, which incorporates substantial deviations from thermal equilibrium at the QCD scale. If axions are used to address the strong CP problem, then the analysis is altered. Depending on the Peccei-Quinn charge assignments, domain walls may be either stable or nonexistent.

Renormalization of the scalar field theory with spontaneously broken discrete symmetry without shifting the field vaccum expectation value

The one-loop renormalization of theλϕ4 theory with a spontaneous breaking of its discrete (reflection) symmetry is analyzed. It is explicitly shown that it is not necessary to forcefully eliminate the linear counterterm in the shifted field (accomplished usually by shifting the vacuum expectation value of the field) in order to have the renormalized Lagrangian still formally invariant under the original discrete symmetry. It is further shown, using the normal-ordering procedure, that the renormalization carried out in the customary form completely wipes out the tadpole diagram contributions from the original Lagrangian. As a consequence, the same renormalized Lagrangian can be also obtained from the original bare Lagrangian which, however, has been normal-ordered and as such cannot cause the linear counterterm in the shifted field since now the tadpole diagrams are absent altogether. These analyses, we believe, should support the view that the vacuum expectation value of the field is of a group-theoretical origin rather than a field-theoretical origin, and as such should not change independently of the shifted field in the course of renormalization.

Green's functions in broken discrete symmetry

Scalar fields with interaction $$\begin{array}{*{20}c} {\lambda \sum\limits_{i \ne j} {\phi i^2 \phi j^2 } } & {or} & {\lambda '\sum\limits_{i,j,k,l pairwise disticnt} {\phi i\phi j\phi k\phi l} } \\ \end{array} $$ are considered in Green's function formalism of quantum field theory. Equations for Green's functions are derived under the assumption that someG2n+1 are not zero. Descending problems from given (modelG3,G4 and fromG4,G5 are discussed, without appealing to perturbation theory.

Comment on a unified theory of weak and strong gravity

In a recent paper CHELA-FLORES (1) considered the unification of the concepts of strong and weak gravity through the use of two scalar fields interacting with the usual 9. tensor gravity. The interaction term in the action is of the form (r + ~ ) R , where ~8 and ~w are the strongand weak-gravity scalars respectively. A correspondence principle was discussed where in the l imit that nuclear forces are negligible (beyond a few femtometers) % << ~w, while in the l imit of strong-gravity dominance ~% << ~08. By gauging the fields as in a theory by FREUND (2), it was shown that the effect of spontaneously broken discrete symmetries C and CP of the gauge field will be of the correct order of magnitude for the reaction Kz-+ 27: in the l imit of strong gravity. This is in opposition to the phenomenological replacement of weak gravity by strong gravity as was done in ref. (2). However there are some problems with the Chela-Flores theory in connection with strong gravity. The scalar field in this limit is supposed to exhibit the Yukawa behavior of the nuclear force. This implies that the field representing strong gravity must be a massive field. On the other hand, the presence of a massive field would spoil the scale invariance of the theory. In this note we would like to show how these remarks can be reconciled by the use of spontaneously broken scale symmetry (a). Due to the presence of a dilaton field (which we identify with the long-range weak-gravity scalar) the masses of particles are spontaneously generated while the overall action remains scale invariant . To demonstrate how this mechanism works we start with the following action in which scale symmetry is explicity broken: