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Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the…
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and…
The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries naturally (unless we engineer fine-tuned toy models to realize higher symmetries). However, for gapped…
A state of matter is characterized by its symmetry breaking and elementary excitations. A supersolid is a state which breaks both translational symmetry and internal $ U(1) $ symmetry. Here, we review some past and recent works in…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
Motivated by an analogy with the conformal factor problem in gravitational theories of the $R+R^2$-type we investigate a $d$-dimensional Euclidean field theory containing a complex scalar field with a quartic self interaction and with a…
A central goal in condensed matter and modern atomic physics is the exploration of many-body quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase…
The spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same structures repeat themselves in time can…
Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of…
Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are…
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding…
Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories,…
Superfluids under specific conditions can exhibit spontaneous breaking of continuous translation symmetries and form exotic spatially ordered states of matter known as supersolids. Despite its early theoretical prediction, it took over…
In condensed matter systems, the atoms, electrons or spins can sometimes arrange themselves in ways that result in unexpected properties but that cannot be detected by conventional experimental probes. Several historical and contemporary…
The existence of a paradoxical supersolid phase of matter, possessing the apparently incompatible properties of crystalline order and superfluidity, was predicted 50 years ago. Solid helium was the natural candidate, but there supersolidity…
Symmetry is central to how we classify phases of matter: solids break spatial translations, superfluids break particle-number conservation, and superconductors "break" gauge symmetry. Mixed anomalies involving higher-form symmetries,…
Spontaneous pattern formation is a phenomenon ubiquitous in nature, examples ranging from Rayleigh-Benard convection to the emergence of complex organisms from a single cell. In physical systems, pattern formation is generally associated…
We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles with an offset center of mass and a non-isotropic inertia tensor. The rolling constraint is considered as a simplified model of a very…
The Standard Model of particle physics is governed by Poincar\'e symmetry, while all other symmetries, exact or approximate, are essentially dictated by theoretical consistency with the particle spectrum. On the other hand, many models of…
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation…