Related papers: Exponential decay in $O(n)$-invariant quantum spin…
We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N > 1. Our result is new when N > 3, in which case no Lee-Yang theorem…
The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model. It has been conjectured that both the spin and the…
We consider an one-dimensional lattice system of unbounded and continuous spins. The Hamiltonian consists of a perturbed strictly-convex single-site potential and with longe-range interaction. We show that if the interactions decay…
We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or…
We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two…
We show that the loop $O(n)$ model on the hexagonal lattice exhibits exponential decay of loop sizes whenever $n> 1$ and $x<\tfrac{1}{\sqrt{3}}+\varepsilon(n)$, for some suitable choice of $\varepsilon(n)>0$. It is expected that, for $n…
We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…
Most quantum system with short-ranged interactions show a fast decay of entanglement with the distance. In this Letter, we focus on the peculiarity of some systems to distribute entanglement between distant parties. Even in realistic…
We establish dimerization in $O(n)$-invariant quantum spin chains with big enough $n$, in a large part of the phase diagram where this result is expected. This includes identifying two distinct ground states which are translations of one…
We show that quantum correlations as quantified by quantum discord can characterize quantum phase transitions by exhibiting nontrivial long-range decay as a function of distance in spin systems. This is rather different from the behavior of…
We study a class of quantum spin systems that includes the $S=\tfrac12$ Heisenberg and XY-models, and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily…
We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as…
The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r^{-\alpha} at large distances r with an exponent $\alpha$ not exceeding the lattice dimension. For a large class of…
We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies. For physical initial states, our bounds predict…
We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric…
We study numerically the damping of quantum oscillations and the increase of entropy with time in model spin systems decohered by a spin bath. In some experimentally relevant cases, the oscillations of considerable amplitude can persist…
Lattice Monte-Carlo simulations were performed to study the equilibrium ordering in a two-dimensional nematic system with quenched random disorder. When the disordering field, which competes against the aligning effect of the Frank…
It is predicted that (i) spin echoes have two kinds of generic long-time decays: either simple exponential, or a superposition of a monotonic and an oscillatory exponential decays; and (ii) the long-time behavior of spin echo and the…
We show that the components of finite energy solutions to general nonlinear Schr\"odinger systems have exponential decay at infinity. Our results apply to positive or sign-changing components, and to cooperative, competitive, or…
The classical spin $O(n)$ model is a model on a $d$-dimensional lattice in which a vector on the $(n-1)$-dimensional sphere is assigned to every lattice site and the vectors at adjacent sites interact ferromagnetically via their inner…