English
Related papers

Related papers: Tree tensor network state approach for solving hie…

200 papers

Simulating quantum systems constructively furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this letter, we directly simulate and explore the entanglement structure present in a…

Quantum Physics · Physics 2017-12-27 Eugene Dumitrescu

The hierarchical equations of motion (HEOM) provide a numerically exact approach for simulating the dynamics of open quantum systems coupled to a harmonic bath. However, its applicability has traditionally been limited to specific spectral…

Quantum Physics · Physics 2023-08-07 Meng Xu , Joachim Ankerhold

This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic…

Quantum Physics · Physics 2025-07-04 Hazar Çakır , Richard M. Milbradt , Christian B. Mendl

A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to…

Quantum Physics · Physics 2023-12-14 Z. Gholami , Z. Noorinejad , M. Amini , E. Ghanbari-Adivi

The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion…

Quantum Physics · Physics 2018-07-18 Wei Wu

One of the approaches used to solve for the dynamics of open quantum systems is the hierarchical equations of motion (HEOM). Although it is numerically exact, this method requires immense computational resources to solve. The objective here…

Quantum Physics · Physics 2022-10-28 Kimara Naicker , Ilya Sinayskiy , Francesco Petruccione

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states…

Strongly Correlated Electrons · Physics 2013-04-09 Naoki Nakatani , Garnet Kin-Lic Chan

The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling…

Chemical Physics · Physics 2022-08-17 Thomas P Fay

The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems that are embedded in thermal environments.…

Quantum Physics · Physics 2025-10-07 Meng Xu , Yaming Yan , Qiang Shi , J. Ankerhold , J. T. Stockburger

We derive an extended version of the hierarchical equations of motion (HEOM) to compute output physical properties of a bosonic environment, which is allowed to be initially prepared at an earlier time in a non-Gaussian input state and then…

Quantum Physics · Physics 2025-08-15 Mauro Cirio , Pengfei Liang , Neill Lambert

We rigorously investigate the quantum non-Markovian dissipative dynamics of a system coupled to a harmonic oscillator bath by deriving hierarchical Schrodinger equations of motion (HSEOM) and studying their dynamics. The HSEOM are the…

Quantum Physics · Physics 2018-07-11 Kiyoto Nakamura , Yoshitaka Tanimura

The Hierarchical Equations of Motion (HEOM) method has become one of the cornerstones in the simulation of open quantum systems and their dynamics. It is commonly referred to as a non-perturbative method. Yet, there are certain instances,…

Quantum Physics · Physics 2024-08-13 Malte Krug , Jürgen Stockburger

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the…

Being able to study the dynamics of quantum systems interacting with several environments is important in many settings ranging from quantum chemistry to quantum thermodynamics, through out-of-equilibrium systems. For such problems tensor…

Quantum Physics · Physics 2025-05-22 Thibaut Lacroix , Brendon W. Lovett , Alex W. Chin

Being a numerically exact method for the simulation of dynamics in open quantum systems, the hierarchical equations of motion (HEOM) still suffers from the curse of dimensionality. In this study, we propose a novel MCE-HEOM method, which…

Chemical Physics · Physics 2025-09-08 Zhecun Shi , Huiqiang Zhou , Lei Huang , Rixin Xie , Linjun Wang

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly…

Strongly Correlated Electrons · Physics 2014-08-04 Dong Hou , Rulin Wang , Xiao Zheng , NingHua Tong , JianHua Wei , YiJing Yan

The Hierarchical equations of motion (HEOM) method is an important non-perturbative technique, allowing numerically exact treatment of open quantum systems with strong coupling and non-Markovian memory. However, its encoding of bath memory…

Quantum Physics · Physics 2026-03-25 Po-Rong Lai , Jhen-Dong Lin , Yi-Te Huang , Po-Chen Kuo , Neill Lambert , Yueh-Nan Chen

Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…

Computational Engineering, Finance, and Science · Computer Science 2026-03-31 Zheng Guo , Aditya Deshpande , Xinyu Wang , Brian C. Kiedrowski , Alex A. Gorodetsky

Open quantum systems that feature non-Markovian dynamics are routinely solved using techniques such as the Hierarchical Equations of Motion (HEOM). However, their usage of the entire system density-matrix renders them intractable for…

Quantum Physics · Physics 2025-06-30 Kai Müller , Kimmo Luoma , Christian Schäfer

Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly…

Quantum Physics · Physics 2023-12-21 Philipp Schmoll , Jan Naumann , Alexander Nietner , Jens Eisert , Spyros Sotiriadis