Showing papers on "Explicit symmetry breaking published in 2020"

The Effective Action of Superrotation Modes

Abstract: Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev--Shatashvili action on the celestial sphere. This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff$(\mathcal{S}^2)$ superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern--Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere.

Diagnosis of explicit symmetry breaking in the tight-binding constructions for symmetry-protected topological systems

Abstract: It has been well established that for symmetry-protected topological systems, the nontrivial topology prevents a real space representation using exponentially localized Wannier wave functions (WFs) in all directions, unless the protecting symmetry is sacrificed as an on-site transformation. This makes it challenging to determine the symmetry of various physical observables represented using such WFs. In this work, we propose a practical method for overcoming such challenges using the Kane-Mele model as a concrete example. We present a systematic procedure for diagnosing the symmetry of any observables, as well as a method for constructing symmetric operators up to arbitrary truncation accuracy.

Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration

Abstract: We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system. Results in the two-dimensional Ising model evidence that the field can induce an order-disorder phase transition by breaking or restoring the symmetry, in contrast with the field of the conventional order parameter which causes explicit symmetry breaking. The critical behavior is then studied by proposing a Hamiltonian-agnostic reweighting approach and forming a renormalization group mapping on quantities derived from the neural network. Accurate estimates of the critical point and of the critical exponents related to the operators that govern the divergence of the correlation length are provided. We conclude by discussing how the method provides an essential step toward bridging machine learning and physics.

Supersymmetry anomaly in the superconformal Wess-Zumino model

Abstract: We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses ${\mathcal N}=1$ superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-loop computation using a supersymmetric Pauli-Villars regulator. The conformal current multiplet does not exist in the regulated theory because the regulator breaks conformal invariance, R-symmetry and S-supersymmetry explicitly. The minimal massive multiplet is the Ferrara-Zumino (FZ) one and the supersymmetry preserved by the regulator is a specific field dependent combination of Q- and S- supersymmetry of the conformal multiplet. While this supersymmetry is non anomalous, conformal invariance, R-symmetry and the original Q- and S-supersymmetries are explicitly broken by finite contact terms, both in the regulated and renormalized theories. A conformal current multiplet does exist for the renormalized theory and may be obtained from the FZ multiplet by a set of finite local counterterms that eliminate the explicit symmetry breaking, thus restoring superconformal invariance up to anomalies. However, this necessarily renders both Q- and S-supersymmetries anomalous, as is manifest starting at 4-point functions of conformal multiplet currents. The paper contains a detailed discussion of a number of issues and subtleties related to Ward identities that may be useful in a wider context.

Relaxation and entropy generation after quenching quantum spin chains

Abstract: This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving Renyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.

Relaxation and entropy generation after quenching quantum spin chains

Abstract: This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving Renyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.

Extended Lipkin-Meshkov-Glick Hamiltonian

Abstract: The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the main features of real physical systems. In the present contribution, we explicitly review the fact that different many-body approximations commonly used in different fields in physics clearly fail to describe the exact LMG solution. With similar assumptions as those adopted for the LMG model, we propose a new Hamiltonian based on a general two-body interaction. The new model (Extended LMG) is not only more general than the original LMG model and, therefore, with a potentially larger spectrum of applicability, but also the physics behind its exact solution can be much better captured by common many-body approximations. At the basis of this improvement lies a new term in the Hamiltonian that depends on the number of constituents of the system and polarizes it, producing an explicit symmetry breaking.

The explicit symmetry breaking solutions of the Kadomtsev–Petviashvili equation

Abstract: To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Backlund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.

Kaons and Antikaons in Multi-Phase Transport Model

Abstract: We investigate the impact of medium modifications of kaons and antikaons on there rapidity distribution and production ratio using A Multi-Phase transport (AMPT) model. The medium modified masses of kaons and antikaons, which are used as input in AMPT model, are calculated using the chiral SU(3) mean field model. Usually in chiral SU(3) models along with the Weinberg Tomozawa term, the contribution of explicit symmetry breaking term and three range terms are considered to evaluate in-medium masses of kaons and antikaons. In the present work, we have considerd Weinberg Tomozawa term and two range terms to study their impact on the above listed experimental observables. The repulsive contribution to the mass of K+ meson from the Weinberg term dominates over the attractive contribution from two range terms. For the K− meson Weinberg term as well as two range terms give attractive contribution. Considering all these features from chiral effective model on properties of K+ and K− mesons, we explore the rapidity distributions of kaons and antikaons.

Corrections to Wigner–Eckart Relations by Spontaneous Symmetry Breaking

Abstract: The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.

Corrections to Wigner-Eckart Relations by Spontaneous Symmetry Breaking

Abstract: The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group $G$ are governed by the well-known Wigner-Eckart relations In the case of infinitely-extended systems, with $G$ spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons An explicit example is discussed, illustrating the two cases