Condensed Matter

Thermalization of random-field Heisenberg spin chain is probed by time evolution of density correlation functions. Studying the impacts of average energies of initial product states on dynamics of the system, we provide arguments in favor of the existence of a mobility edge in the large system-size limit.

We analyze the localization properties of the disordered Hubbard model in the presence of a synthetic magnetic field. An analysis of level spacing ratio shows a clear transition from ergodic to many-body localized phase. The transition shifts to larger disorder strengths with increasing magnetic flux. Study of dynamics of local correlations and entanglement entropy indicates that charge excitations remain localized whereas spin degree of freedom gets delocalized in the presence of the synthetic flux. This residual ergodicity is enhanced by the presence of the magnetic field with dynamical observables suggesting incomplete localization at large disorder strengths. Furthermore, we examine the effect of quantum statistics on the local correlations and show that the long-time spin oscillations of a hard-core boson system are destroyed as opposed to the fermionic case.

Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We explore the implications of NISQ platforms for many-body physics in a practical sense: we ask which {\it physical phenomena}, in the domain of quantum statistical mechanics, they may realize more readily than traditional experimental platforms. As a particularly well-suited target, we identify discrete time crystals (DTCs), novel non-equilibrium states of matter that break time translation symmetry. These can only be realized in the intrinsically out-of-equilibrium setting of periodically driven quantum systems stabilized by disorder induced many-body localization. While precursors of the DTC have been observed across a variety of experimental platforms - ranging from trapped ions to nitrogen vacancy centers to NMR crystals - none have \emph{all} the necessary ingredients for realizing a fully-fledged incarnation of this phase, and for detecting its signature long-range \emph{spatiotemporal order}. We show that a new generation of quantum simulators can be programmed to realize the DTC phase and to experimentally detect its dynamical properties, a task requiring extensive capabilities for programmability, initialization and read-out. Specifically, the architecture of Google's Sycamore processor is a remarkably close match for the task at hand. We also discuss the effects of environmental decoherence, and how they can be distinguished from `internal' decoherence coming from closed-system thermalization dynamics. Already with existing technology and noise levels, we find that DTC spatiotemporal order would be observable over hundreds of periods, with parametric improvements to come as the hardware advances.

Random K -satisfiability ( K -SAT) is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms. The statistical properties of the random K -SAT solution space have been extensively investigated, but most earlier efforts focused on solutions that are typical. Here we consider maximally flexible solutions which satisfy all the constraints only using the minimum number of variables. Such atypical solutions have high internal entropy because they contain a maximum number of null variables which are completely free to choose their states. Each maximally flexible solution indicates a dense region of the solution space. We estimate the maximum fraction of null variables by the replica-symmetric cavity method, and implement message-passing algorithms to construct maximally flexible solutions for single K -SAT instances.

We evaluate the typical ARA performance of the CDMA multiuser detection by means of statistical mechanics using the replica method. At first, we consider the oracle cases where the initial candidate solution is randomly generated with a fixed fraction of the original signal in the initial state. In the oracle cases, the first-order phase transition can be avoided or mitigated by ARA if we prepare for the proper initial candidate solution. We validate our theoretical analysis with quantum Monte Carlo simulations. The theoretical results to avoid the first-order phase transition are consistent with the numerical results. Next, we consider the practical cases where we prepare for the initial candidate solution obtained by commonly used algorithms. We show that the practical algorithms can exceed the threshold to avoid the first-order phase transition. Finally, we test the performance of ARA with the initial candidate solution obtained by the practical algorithm. In this case, the ARA can not avoid the first-order phase transition even if the initial candidate solution exceeds the threshold to avoid the first-order phase transition.

The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, d?��? limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently suggested that as d increases the behavior of the RLG converges to the glassy description, and that percolation physics is recovered thanks to finite- d perturbative and non-perturbative (instantonic) corrections [Biroli et al. arXiv:2003.11179]. Here, we expand on the d?��? physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/d correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the d?��? RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.

We consider a class of random block matrix models in d dimensions, d≥1 , motivated by the study of the vibrational density of states (DOS) of soft spheres near the isostatic point. The contact networks of average degree Z= z 0 +ζ are represented by random z 0 -regular graphs (only the circle graph in d=1 with z 0 =2 ) to which Erdös-Renyi graphs having a small average degree ζ are superimposed. In the case d=1 , for ζ small the shifted Kesten-McKay DOS with parameter Z is a mean-field solution for the DOS. Numerical simulations in the z 0 =2 model, which is the k=1 Newman-Watts small-world model, and in the z 0 =3 model lead us to conjecture that for ζ→0 the cumulative function of the DOS converges uniformly to that of the shifted Kesten-McKay DOS, in an interval [0, ω 0 ] , with ω 0 < z 0 −1 − − − − − √ +1 . For 2≤d≤4 , we introduce a cutoff parameter K d ≤0.5 modeling sphere repulsion. The case K d =0 is the random elastic network case, with the DOS close to the Marchenko-Pastur DOS with parameter t= Z d . For K d large the DOS is close for small ω to the shifted Kesten-McKay DOS with parameter t= Z d ; in the isostatic case the DOS has around ω=0 the expected plateau. The boson peak frequency in d=3 with K 3 large is close to the one found in molecular dynamics simulations for Z=7 and 8 .

In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol as recently introduced in Ref. [1], which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the infinite-dimension limit, the mean-field dynamics under such a random forcing is strictly equivalent to that under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements on interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. We discuss specifically the implications on the quasistatic driving of glasses -- initially prepared at a replica-symmetric equilibrium -- and how the corresponding 'stress-strain'-like curves and the elastic moduli can be rescaled onto their quasistatic-shear counterparts. These results hint at a unifying framework for establishing rigourous analogies, at the mean-field level, between different driven disordered systems.

The correlation kinetic equation approach is developed that allows describing spin correlations in a material with hopping transport. The quantum nature of spin is taken into account. The approach is applied to the problem of the bipolaron mechanism of organic magnetoresistance (OMAR) in the limit of large Hubbard energy and small applied electric field. The spin relaxation that is important to magnetoresistance is considered to be due to hyperfine interaction with atomic nuclei. It is shown that the lineshape of magnetoresistance depends on short-range transport properties. Different model systems with identical hyperfine interaction but different statistics of electron hops lead to different lineshapes of magnetoresistance including the two empirical laws H 2 /( H 2 + H 2 0 ) and H 2 /(|H|+ H 0 ) 2 that are commonly used to fit experimental results.

We study the free energy of a most used deep architecture for restricted Boltzmann machines, where the layers are disposed in series. Assuming independent Gaussian distributed random weights, we show that the error term in the so-called replica symmetric sum rule can be optimised as a saddle point. This leads us to conjecture that in the replica symmetric approximation the free energy is given by a min max formula, which parallels the one achieved for two-layer case.