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We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters…
We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum…
The renormalization group approach to correlated fermions is used to determine the phase diagram of the oxide cuprates modeled by the t-t' Hubbard model at the Van Hove filling. Spin-dependent interactions give rise to instabilities…
We study the bipartite von Neumann entropy of two particles interacting via a long-range scale-free potential $V(r)\sim -g/r^2$ in three dimensions, close to the unbinding transition. The nature of the quantum phase transition changes from…
Due to intrinsic frustrations of interaction, the 2d Ising model with competing ferromagnetic short-range nearest-neighbour and antiferromagnetic long-range dipole interactions possesses a rich phase diagram. The order of the phase…
Holographic RG flows dual to QFTs on maximally symmetric curved manifolds (dS$_d$, AdS$_d$, and $S^d$) are considered in the framework of Einstein-dilaton gravity in $d+1$ dimensions. A general dilaton potential is used and the flows are…
It is beyond the present techniques based on perturbation theory to reveal the nature of phase transitions in strongly interacting field theories. Recently, the holographic approach has provided us with an effective dual description,…
Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the…
Considering a doubly holographic model, we study the black hole information paradox for the eternal AdSd-RN black hole coupled to and in equilibrium with a d-dimensional conformal bath whose state has been deformed by the charged scalar…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a…
For $N$ interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the ``sites''. The hopping terms are induced by the…
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in…
Density Matrix Renormalization Group (DMRG) calculations on 4-leg t-J and Hubbard ladders have found a phase exhibiting "stripes" at intermediate doping. Such behavior can be viewed as generalized Friedel oscillations, with wavelength equal…
Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
Although ubiquitous, interactions of groups of individuals (e.g., modern messaging applications, group meetings, or even a parliament discussion) are not yet thoroughly studied. Frequently, single-groups are modeled as critical-mass…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
We re-examine the band structure of the stripe charge ordered state of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure by using an extended Hubbard model within the Hartree mean-field theory. By increasing pressure, we find a topological…
The binomial random bipartite graph $G(n,n,p)$ is the random graph formed by taking two partition classes of size $n$ and including each edge between them independently with probability $p$. It is known that this model exhibits a similar…