Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder

Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold

We consider the simplest inhomogeneous Matrix-Product-State for an open chain of N quantum spins that involves only two angles per site and two angles per bond with the following direct physical meanings. The two angles associated to the site $k$ are the two Bloch angles that parametrize the two orthonormal eigenvectors of the reduced density matrix $ρ_k$ of the spin $k$ alone. The two angles associated to the bond $(k,k+1)$ parametrize the entanglement properties of the Schmidt decomposition across the bond $(k,k+1)$. Explicit results are given for the reduced density matrix $ρ_{k,k+1}$ of tw…

Ballistic transport in random magnetic fields with anisotropic long-ranged correlations

We present exact theoretical results about energetic and dynamic properties of a spinless charged quantum particle on the Euclidean plane subjected to a perpendicular random magnetic field of Gaussian type with non-zero mean. Our results refer to the simplifying but remarkably illuminating limiting case of an infinite correlation length along one direction and a finite but strictly positive correlation length along the perpendicular direction in the plane. They are therefore ``random analogs'' of results first obtained by A. Iwatsuka in 1985 and by J. E. Müller in 1992, which are greatly estee…

Learning intermolecular forces at liquid-vapor interfaces

By adopting a perspective informed by contemporary liquid state theory, we consider how to train an artificial neural network potential to describe inhomogeneous, disordered systems. We find that neural network potentials based on local representations of atomic environments are capable of describing some properties of liquid-vapor interfaces, but typically fail for properties that depend on unbalanced long-ranged interactions which build up in the presence of broken translation symmetry. These same interactions cancel in the translationally invariant bulk, allowing local neural network potent…

Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation

For a given inhomogeneous exclusion processes on $N$ sites between two reservoirs, the trajectories probabilities allow to identify the relevant local empirical observables and to obtain the corresponding rate function at Level 2.5. In order to close the hierarchy of the empirical dynamics that appear in the stationarity constraints, we consider the simplest approximation, namely the Mean-Field approximation for the empirical density of two consecutive sites, in direct correspondence with the previously studied Mean-Field approximation for the steady state. For a given inhomogeneous Totally As…

Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets

We investigate quantum phase transitions in the spin-1/2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a novel quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating…

无序量子自旋链的Fock空间上的概率输运

Probability transport on the Fock space of a disordered quantum spin chain

本文研究无序量子自旋链Fock空间上的概率输运，揭示遍历相与多体局域化相在动力学均匀性和多重分形行为上的本质差异，并建立动力学长度尺度与自旋自关联衰减之间的联系。