Related papers: Inchworm tensor train hybridization expansion quan…
The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this challenge…
Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to…
We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign…
We propose an efficient tensor-train-based algorithm for simulating open quantum systems with the inchworm method, where the reduced dynamics of the open quantum system is expressed as a perturbative series of high-dimensional integrals.…
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…
We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all…
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…
The Grassmann time-evolving matrix product operator method has shown great potential as a general-purpose quantum impurity solver, as its numerical errors can be well-controlled and it is flexible to be applied on both the imaginary- and…
The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive,…
We discuss the evaluation of the integrals for intermediate-order diagrams in the self-consistent strong-coupling expansion on the Keldysh contour using Tensor Cross Interpolation (TCI). TCI is used to factorize the nested parts of the…
The polaron problem is a very old problem in condensed matter physics that dates back to the thirties, but still remain largely unsolved today, especially when electron-electron interaction is taken into consideration. The presence of both…
Numerical methods capable of handling nonequilibrium impurity models are essential for the study of transport problems and the solution of the nonequilibrium dynamical mean field theory (DMFT) equations. In the strong correlation regime,…
Quantized tensor trains (QTTs) are a multiscale computational framework that can potentially reduce the computational cost of solving partial differential equations and initial value problems by making low-rank approximations. However, its…
We introduce a tree tensor network (TTN) impurity solver that enables highly efficient and accurate real-time simulations of quantum impurity models. By decomposing a noninteracting bath Hamiltonian into a Cayley tree, the method provides a…
Strongly correlated quantum impurity problems appear in a wide variety of contexts ranging from nanoscience and surface physics to material science and the theory of strongly correlated lattice models, where they appear as auxiliary systems…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
We apply the tensor cross interpolation (TCI) algorithm to solve equilibrium quantum impurity problems with high precision based on the weak-coupling expansion. The TCI algorithm, a kind of active learning method, factorizes…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…
Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid…