Related papers: Numerical continuum tensor networks in two dimensi…
We demonstrate the power of 2D tensor networks for obtaining large deviation functions of dynamical observables in a classical nonequilibrium setting. Using these methods, we analyze the previously unstudied dynamical phase behavior of the…
We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
We consider the two-dimensional Fermi gas at finite temperature with attractive short-range interactions. Using the virial expansion, which provides a controlled approach at high temperatures, we determine the spectral function and contact…
We study induced pairing between two identical fermions mediated by an attractively interacting quantum impurity in two-dimensional systems. Based on a Stochastic Variational Method (SVM), we investigate the influence of confinement and…
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
We study the dynamical fermionization of strongly interacting one-dimensional bosons in Tonks-Girardeau limit by solving the time dependent many-boson Schr\"odinger equation numerically exactly. We establish that the one-body momentum…
The Gross-Pitaevskii equation and its generalisations to dissipative and dipolar gases have been very useful in describing dynamics of cold atomic gases, as well as polaritons and other nonlinear systems. For some of these applications the…
Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and…
We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field…
This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…
We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block…
We analyze the recently developed folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] to simulate the dynamics of infinite quantum spin chains, and relate its performance to the kind of entanglement produced under the evolution of…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…