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Tower of States analysis is a powerful tool for investigating phase transitions in condensed matter systems. Spontaneous symmetry breaking implies a specific structure of the energy eigenvalues and their corresponding quantum numbers on…
The study of critical phenomena and phase transitions is an important part of modern condensed matter physics. In this regard, the phenomenological Landau theory has been extraordinarily useful. Hereby we present an alternative theoretical…
We determine when a permutation with cycle type $\mu$ admits a non-zero invariant vector in the irreducible representation $V_\lambda$ of the symmetric group. We find that a majority of pairs $(\lambda,\mu)$ have this property, with only a…
We determine semisimple reductions of irreducible, 2-dimensional crystalline representations of the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_{p^f})$. To this end, we provide explicit representatives for the…
Crystal symmetry plays a fundamental role in determining its physical, chemical, and electronic properties such as electrical and thermal conductivity, optical and polarization behavior, and mechanical strength. Almost all known crystalline…
We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for…
We construct an explicit sequence $V_{k_n,a_n}$ of crystalline representations of exceptional weights converging to a given irreducible two-dimensional semi-stable representation $V_{k,{\mathcal{L}}}$ of…
In this work, we explore the dynamics of time varying photonic media with an optical Kerr nonlinearity and an associated phase transition. The interplay between a periodically modulated permittivity and the nonlinearity induces a continuous…
Astrophysical observations of neutron stars probe the structure of dense nuclear matter and have the potential to reveal phase transitions at high densities. Most recent analyses are based on parametrized models of the equation of state…
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the…
We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be…
Crystals are the foundation of numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods seldom consider the space group constraint which is crucial…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…
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…
Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantum supermembrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group $G$ is split (or…
The aim of this paper is to propose a criterion of spontaneous symmetry breaking that makes reference to the properties of pure phases defined by a translationally invariant state. By avoiding any reference to the ground state, at the basis…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
Hexagonal lattice systems (e.g. triangular, honeycomb, kagome) possess a multidimensional irreducible representation corresponding to $d_{x^2-y^2}$ and $d_{xy}$ symmetry. Consequently, various unconventional phases that combine these…
A Python program for calculating the metrics necessary to perform information-theory based symmetry classifications and quantifications of transmission electron diffraction spot patterns is introduced. It is the first of its kind, in that…
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…