Related papers: Matrix Product State and mean field solutions for …
Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization,…
A simple, general and practically exact method is developed to calculate the ground states of 1D macroscopic quantum systems with translational symmetry. Applied to the Hubbard model, a modest calculation reproduces the Bethe Ansatz…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product…
We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
In this paper we prove the nonlinear orbital stability of a large class of steady states solutions to the Hamiltonian Mean Field (HMF) system with a Poisson interaction potential. These steady states are obtained as minimizers of an energy…
Using the matrix product ansatz, we obtain solutions of the steady-state distribution of the two-species open one-dimensional zero range process. Our solution is based on a conventionally employed constraint on the hop rates, which…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
We investigate the application of matrix product states to the Hubbard model in one spatial dimension with both of open and periodic boundary conditions. We develop the variatinal method that the optimization of the variational parameters…
By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new…
The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis,…
Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the…
We solve the mixing-demixing transition in repulsive one-dimensional bose-bose mixtures. This is done numerically by means of the continuous matrix product states variational ansatz. We show that the effective low-energy bosonization theory…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from…
Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…