Condensed Matter

We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of k -uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between variables belonging to distinct hyperedges. We show that the threshold α d (k) for the transition can be further increased with respect to a restricted interaction within the hyperedges, and perform an asymptotic expansion of α d (k) in the large k limit. We find that α d (k)= 2 k−1 k (lnk+lnlnk+ γ d +o(1)) , where the constant γ d is strictly larger than for the uniform measure over solutions.

We present a simple model of the bimolecular charge carrier recombination in polar amorphous organic semiconductors where the dominant part of the energetic disorder is provided by permanent dipoles and show that the recombination rate constant could be much smaller than the corresponding Langevin rate constant. The reason for the strong decrease of the rate constant is the long range spatial correlation of the random energy landscape in amorphous dipolar materials, without spatial correlation even strong disorder does not modify the Langevin rate constant. Our study shows that the significant suppression of the bimolecular recombination could take place in homogeneous amorphous organic semiconductors and does not need large scale inhomogeneity of the material.

We consider a percolation process in which k points separated by a distance proportional to system size L simultaneously connect together ( k>1 ), or a single point at the center of a system connects to the boundary ( k=1 ), through adjacent connected points of a single cluster. These processes yield new thresholds p ¯ ¯ ¯ ck defined as the average value of p at which the desired connections first occur. These thresholds are not sharp as the distribution of values of p ck for individual samples remains broad in the limit of L→∞ . We study p ¯ ¯ ¯ ck for bond percolation on the square lattice, and find that p ¯ ¯ ¯ ck are above the normal percolation threshold p c =1/2 and represent specific supercritical states. The p ¯ ¯ ¯ ck can be related to integrals over powers of the function P ∞ (p) equal to the probability a point is connected to the infinite cluster; we find numerically from both direct simulations and from measurements of P ∞ (p) on L×L systems that, for L→∞ , p ¯ ¯ ¯ c1 =0.51755(5) , p ¯ ¯ ¯ c2 =0.53219(5) , p ¯ ¯ ¯ c3 =0.54456(5) , and p ¯ ¯ ¯ c4 =0.55527(5). The percolation thresholds p ¯ ¯ ¯ ck remain the same, even when the k points are randomly selected within the lattice. We show that the finite-size corrections scale as L −1/ ν k where ν k =ν/(kβ+1) , with β=5/36 and ν=4/3 being the ordinary percolation critical exponents, so that ν 1 =48/41 , ν 2 =24/23 , ν 3 =16/17 , ν 4 =6/7 , etc. We also study three-point correlations in the system, and show how for p> p c , the correlation ratio goes to 1 (no net correlation) as L→∞ , while at p c it reaches the known value of 1.022.

We study bond percolation on the simple cubic (SC) lattice with various combinations of first, second, third, and fourth nearest-neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the bond thresholds. Correlations between percolation thresholds and lattice properties are discussed, and our results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power law p c ∼ z −a , with exponent a=1.111 . However, for large z , the threshold must approach the Bethe lattice result p c =1/(z−1) . Fitting our data and data for lattices with additional nearest neighbors, we find p c (z−1)=1+1.224 z −1/2 .

We study the properties of a homogeneous dilute Bose-Bose gas in a weak-disorder potential at zero temperature. By using the perturbation theory, we calculate the disorder corrections to the condensate density, the equation of state, the compressibility, and the superfluid density as a function of density, strength of disorder, and miscibility parameter. It is found that the disorder potential may lead to modifying the miscibility-immiscibility condition and a full miscible phase turns out to be impossible in the presence of the disorder. We show that the intriguing interplay of the disorder and intra- and interspecies interactions may strongly influence the localization of each component, the quantum fluctuations, and the compressibility, as well as the superfluidity of the system.

We study a non-Hermitian Aubry-André-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single-particle states are asymmetrically localized due to non-Hermitian skin effect and have energy-independent localization lengths. We also discuss possible experimental detections of our results in electric circuits.

Entanglement in a pure state of a many-body system can be characterized by the Rényi entropies S (α) =lntr( ρ α )/(1−α) of the reduced density matrix ρ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, ln S (2) can be tightly bound by the much easier accessible Rényi number entropy S (2) N =−ln ∑ n p 2 (n) which is a function of the probability distribution p(n) of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth---albeit logarithmically slower---of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal disorder.

The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in the majority of cases sizes can not be varied at will. Here we discuss how finite-size scaling can be approximated in an experimental system of fixed and relatively small size by computing correlations inside of a reduced field of view of various sizes (i.e., "box-scaling"). Numerical simulations of a neuronal network are used to verify such approximation, as well as the ferromagnetic 2D Ising model. The numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breakings in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

The three-dimensional Edwards-Anderson spin-glass model present strong spatial heterogeneities well characterized by the so-called backbone, a magnetic structure that arises as a consequence of the properties of the ground state and the low-excitation levels of such a frustrated Ising system. Using extensive Monte Carlo simulations and finite size scaling, we study how these heterogeneities affect the phase transition of the model. Although, we do not detect any significant difference between the critical behavior displayed by the whole system and that observed inside and outside the backbone, surprisingly, a selective bond dilution of the complement of this magnetic structure induces a change of the universality class, whereas no change is noted when the backbone is fully diluted. This finding suggests that the region surrounding the backbone plays a more relevant role in determining the physical properties of the Edwards-Anderson spin-glass model than previously thought. Furthermore, we show that when a selective bond dilution changes the universality class of the phase transition, the ground state of the model does not undergo any change. The opposite case is also valid, i. e., a dilution that does not change the critical behavior significantly affects the fundamental level.