Related papers: Critical phenomena and phase sequence in classical…
The crystallographic restriction theorem constrains two-dimensional nematicity to display either Ising ($Z_{2}$) or three-state-Potts ($Z_{3}$) critical behaviors, both of which are dominated by amplitude fluctuations. Here, we use group…
We introduce a one-parameter family, $0 \leq H \leq 1$, of pair potential functions with a single relative energy minimum that stabilize a range of vacancy-riddled crystals as ground states. The "quintic potential" is a short-ranged,…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
As a continuation of \cite{me}, we consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger system with a parameter $a $ and the Coulomb potential $V(x)$ in the $L^2$-critical case, where $a>0$ represents the attractive…
Transition metal dichalcogenides (TMDs) constitute an intriguing platform for studying charge-ordered states including conventional and generalized Wigner crystals as well as Mott insulating states. In this work, we combine a phonon mode…
When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x-y), highly correlated states emerge as a result of the interplay between electron-electron interactions, confinement and…
We study the structure and melting of a classical bilayer system of dipoles, in a setup where the dipoles are oriented perpendicular to the planes of the layers and the density of dipoles is the same in each layer. Due to the anisotropic…
Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By…
We consider temperature-induced melting of a Wigner solid in one dimensional (1D) and two dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged…
We obtain the phase diagram of the double-exchange model at low electronic densities in the presence of electron-electron interactions. The single particle problem and its extension to low electronic densities, when a Wigner crystal of…
The quasi-harmonic model proposes that a crystal can be modeled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss' law shows that the ion-ion potential for a cubic Coulomb…
We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent sign-alternating potentials. In a continuum description, the latter supply the fermions with spin-dependent "relativistic" masses…
We study the structural properties of a quasi-one-dimensional classical Wigner crystal, confined in the transverse direction by a parabolic potential. With increasing density, the one-dimensional crystal first splits into a zigzag crystal…
We theoretically consider two-dimensional moir\'e transition metal dichalcogenide (TMD) bilayers, which are strongly correlated in the sense that the on-site Coulomb interaction is comparable to or larger than the hopping kinetic energy…
Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in $U>0$ Hubbard model including the {\it next nearest neighbor coupling} are calculated with the emphasis on the…
We study the consequences of Coulomb interactions on a system undergoing a putative first order phase transition. In two dimensions (2D), near the critical density, the system is universally unstable to the formation of new intermediate…
Using an ansatz wave function for the ground state of rotating two-dimensional dipolar fermions, which occupy only partially the lowest Landau level, we study the correlation energy and elastic properties of the Wigner crystal of rotating…
We study the phase diagram of the Dicke model in terms of the excitation energy and the radiation-matter coupling constant $\lambda$. Below a certain critical value $\lambda_c$ of the coupling constant $\lambda$ all the energy levels have a…
We investigate the low density limit of the Homogeneous Electron system, often called the {\it Strictly Correlated} regime. We begin with a systematic presentation of the expansion around infinite $r_S$, based on the first quantized…
We experimentally study the critical properties of the non-equilibrium solid-liquid-like transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the…