Spontaneous Breaking Of Discrete Symmetry Research Articles

Domain Formation Driven by the Entropy of Topological Edge Modes.

In this Letter we study interacting systems with spontaneous discrete symmetry breaking, where the degenerate symmetry-broken states are topologically distinct gapped phases. Edge modes appear at domain walls between the two topological phases. In the presence of a weak disorder field conjugate to the order parameter, we find that the entropy of the edge modes drives a thermal transition between a gapped uniform phase and a phase with a disorder-induced domain structure. We characterize this transition using a phenomenological Landau functional, and corroborate our conclusions with a concrete microscopic model. Finally, we discuss the possibilities of experimental signatures of this phase transition, and propose graphene-based moiré heterostructures as candidate materials in which such a phase transition can be detected.

Classical three rotor problem: Periodic solutions, stability and chaos.

This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine interparticle potentials. This system arises as the classical limit of a model of coupled Josephson junctions. In appropriate units, the non-negative energy E of the relative motion is the only free parameter. We find families of periodic solutions: pendulum and isosceles solutions at all energies and choreographies up to moderate energies. The model displays order-chaos-order behavior: it is integrable at zero and infinitely high energies but displays a fairly sharp transition from regular to chaotic behavior as E is increased beyond Ec≈4 and a more gradual return to regularity. The transition to chaos is manifested in a dramatic rise of the fraction of the area of the Hill region of Poincaré surfaces occupied by chaotic sections and also in the spontaneous breaking of discrete symmetries of Poincaré sections present at lower energies. Interestingly, the above pendulum solutions alternate between being stable and unstable, with the transition energies cascading geometrically from either sides at E=4. The transition to chaos is also reflected in the curvature of the Jacobi-Maupertuis metric that ceases to be everywhere positive when E exceeds four. Examination of Poincaré sections also indicates global chaos in a band of energies (5.33≲E≲5.6) slightly above this transition.

Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice $\pi/2$-rotation symmetry. A superposition of SU(2)-symmetric PEPS tensors belonging to two irreducible representations of the lattice point group is shown to capture accurately the properties of the nematic phase, as shown from a comparison to Exact Diagonalisations and Density Matrix Renormalization Group results.

Interacting lattice systems with quantum dissipation: A quantum Monte Carlo study

Quantum dissipation arises when a large system can be split in a quantum system and an environment where the energy of the former flows to. Understanding the effect of dissipation on quantum many-body systems is of particular importance due to its potential relations with quantum information processing. We propose a conceptually simple approach to introduce the dissipation into interacting quantum systems in a thermodynamical context, in which every site of a 1d lattice is coupled off-diagonally to its own bath. The interplay between quantum dissipation and interactions gives rise to counterintuitive interpretations such as a compressible zero-temperature state with spontaneous discrete symmetry breaking and a thermal phase transition in a one-dimensional dissipative quantum many-body system as revealed by Quantum Monte Carlo path integral simulations.

Holographic partition functions and phases for higher genus Riemann surfaces

We describe a numerical method to compute the action of Euclidean saddle points for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.

Spontaneous parity breaking, gauge coupling unification, and consistent cosmology with transitory domain walls

The formation of transitory domain walls is quite generic in theories with spontaneous breaking of discrete symmetries. Since these walls are in conflict with cosmology, there has to be some mechanism which makes them disappear. We study one such mechanism by incorporating Planck-scale suppressed operators within the framework of left-right symmetric models where left-right parity (D parity) is spontaneously broken. We find that this mechanism cannot make the walls disappear in minimal versions of left-right symmetric models. We propose two viable extensions of this model and show that Planck-scale suppressed operators can give rise to the successful disappearance of domain walls provided the scale of parity breaking obeys certain limits. We also constrain the scale of parity breaking by demanding successful gauge-coupling unification and make a comparison of the unification and cosmology bounds.

Phase Transition in Potts Model with Invisible States

We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and the free energy, although they do not contribute to the internal energy. The internal energy and the number of degenerated ground states do not change, if invisible states are introduced into the standard Potts model. A second-order phase transition takes place at finite temperature in the standard $q$-state ferromagnetic Potts model on two-dimensional lattice for $q=2,3$, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous $q$-fold symmetry breaking ($q=2,3$, and 4) due to entropy effect of invisible states. We believe that our present model is a fundamental model for analysis of a first-order phase transition with spontaneous discrete symmetry breaking.

Breaking discrete symmetries in broken gauge theories

We study the spontaneous breaking of discrete symmetries in theories with broken gauge symmetry. The intended application is to CP breaking in theories with gauged flavor symmetries, but the analysis described here is preliminary. We dispense with matter fields and take the gauge theory to be weakly coupled and broken spontaneously by unspecified, short-distance forces. We develop an effective-field-theory description of the resultant low energy theory, and ask whether this theory by itself can describe the subsequent breaking of discrete symmetries. We conclude that this can happen depending on the parameters of the effective theory, and that the intrinsic violation is naturally of order unity.

Kink-induced symmetry breaking patterns in brane-worldSU(3)3trinification models

The trinification grand unified theory (GUT) has gauge group $SU(3{)}^{3}$ and a discrete symmetry permuting the $SU(3)$ factors. In common with other GUTs, the attractive nature of the fermionic multiplet assignments is obviated by the complicated multiparameter Higgs potential apparently needed for phenomenological reasons, and also by vacuum expectation value (VEV) hierarchies within a given multiplet. This motivates the rigorous consideration of Higgs potentials, symmetry breaking patterns, and alternative symmetry breaking mechanisms in models with this gauge group. Specifically, we study the recently proposed ``clash of symmetries'' brane-world mechanism to see if it can help with the symmetry breaking conundrum. This requires a detailed analysis of Higgs potential global minima and kink or domain wall solutions interpolating between the disconnected global minima created through spontaneous discrete symmetry breaking. Sufficiently long-lived metastable kinks can also be considered. We develop what we think is an interesting, albeit speculative, brane-world scheme whereby the hierarchical symmetry breaking cascade, trinification to left-right symmetry to the standard model to color cross electromagnetism, may be induced without an initial hierarchy in vacuum expectation values. Another motivation for this paper is simply to continue the exploration of the rich class of kinks arising in models that are invariant under both discrete and continuous symmetries.

Spontaneous discrete symmetry breaking during inflation and the NMSSM domain wall problem

The Next to Minimal Supersymmetric Standard Model (NMSSM), proposed as a solution of the μ problem of the minimal Supersymmetric Standard Model, has a discrete Z 3 symmetry which is spontaneously broken at the electroweak phase transition, resulting in a cosmological domain wall problem. In most cases this domain wall problem cannot be solved by explicit Z 3 breaking without introducing supergravity tadpole corrections which destabilize the weak scale hierarchy. Here we consider the possibility of solving the domain wall problem of the NMSSM via spontaneous discrete symmetry breaking occurring during inflation. For the case where the discrete symmetry breaking field has renormalizable couplings to the NMSSM fields, we find that the couplings must be less than 10 −5 if the reheating temperature is larger than 10 7 GeV, but can be up to 10 −3 for reheating temperatures of the order of the electroweak phase transition temperature. For the case of non-renormalizable couplings, we present a model which can solve the domain wall problem for large reheating temperatures without requiring any very small coupling constants. In this model the domain walls are eliminated by a pressure coming from their interaction with a coherently oscillating scalar field whose phase is fixed during inflation. This oscillating scalar field typically decays after the electroweak phase transition but before nucleosynthesis, leaving no additional Z 3 symmetry breaking in the zero-temperature theory.

Gravity and the domain-wall problem.

It is well known that the spontaneous breaking of discrete symmetries may lead to a conflict with big-bang cosmology. This is due to the formation of domain walls which give an unacceptable contribution to the energy density of the Universe. On the other hand it is expected that gravity breaks global symmetries explicitly. In this work we propose that this could provide a natural solution to the domain-wall problem.

Coordinate-dependent compactifications and discrete symmetries

We show how coordinate-dependent compactifications provide a generalization of the continuous deformations of free-field vacua of superstrings to extra, discrete ones. These correspond to spontaneous breaking of discrete symmetries, and also have applications to spontaneous supersymmetry breaking, for which we give a general, model-independent discussion, and a number of examples. A particular type of these discrete deformations turns out to be adequate to the study of the finite-temperature statistics of any superstring model, for which we give a simple, explicit and practical prescription.

Spontaneous breaking of discrete symmetries and the semiclassical approximation

The generating functional $Z(j)\ensuremath{\equiv}{〈0|0〉}_{j}$ is evaluated asymptotically as $\ensuremath{\hbar}\ensuremath{\rightarrow}0$ with special attention to the existence of several extremal points of the action. We show that $Z(j)\ensuremath{\sim}N\ensuremath{\Sigma}{\ensuremath{\alpha}}^{}\mathrm{exp}[(\frac{i}{\ensuremath{\hbar}}){W}_{\ensuremath{\alpha}}(j)]$, where $\ensuremath{\alpha}$ labels the extremal points. Here each ${W}_{\ensuremath{\alpha}}$ has a Taylor expansion in $\ensuremath{\hbar}$, Some implications and interpretations of this new result are given.