Related papers: Simple Glass Models and their Quantum Annealing
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
We consider a generalized version of the Random Energy Model in which the energy of each configuration is given by the sum of $N$ independent contributions ("local energies") with finite variances but otherwise arbitrary statistics. Using…
Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding…
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal…
Understanding structural glasses using the Random First Order Transition theory requires a description in both real space and in time, taking into account sample history. A variety of nonlinear objects enter this description, in field…
We study large deviations of the dynamical activity in the random orthogonal model (ROM). This is a fully connected spin-glass model with one-step replica symmetry breaking behaviour, consistent with the random first-order transition…
We study the quantum version of a lattice model whose classical counterpart captures the physics of structural glasses. We discuss the role of quantum fluctuations in such systems and in particular their interplay with the amorphous order…
We report on a remarkable spectral phenomenon in a generic type of quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize and lead to plateaus of the interaction energy, with gaps opening akin…
We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically-constrained models of classical glasses. Through a combination of analytics, exact diagonalization and…
We study the energy gap between the ground state and the first excited state of a mean-field-type non-stoquastic Hamiltonian by a semi-classical analysis. The fully connected mean-field model with $p$-body ferromagnetic interactions under a…
We investigate the liquid-glass phase transition in a system of point-like particles interacting via a finite-range attractive potential in D-dimensional space. The phase transition is driven by an `entropy crisis' where the available phase…
A system of neutral atoms trapped in an optical lattice and dispersively coupled to the field of an optical cavity can realize a variation of the Bose-Hubbard model with infinite-range interactions. This model exhibits a first order quantum…
We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random…
We discuss the possibility of spin glass order in the vicinity of the unexpected metallic state of the two-dimensional electron gas in zero applied magnetic field. An average ferromagnetic moment may also be present, and the spin glass…
We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the…
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series…
The quantum-classical transitions of the escape rates in a uniaxial spin model relevant to the molecular magnet Mn$_{12}$Ac and a biaxial anisotropic ferromagnetic particle are investigated by applying the periodic instanton method. The…
Real life quantum computers are inevitably affected by intrinsic noise resulting in dissipative non-unitary dynamics realized by these devices. We consider an open system quantum annealing algorithm optimized for a realistic analog quantum…