Efficient mapping for Anderson impurity problems with matrix product states

Kohn, Lucas; Santoro, Giuseppe E.

doi:10.1103/physrevb.104.014303

Cited by 22 publications

(34 citation statements)

References 59 publications

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“…For more details and the extension to finite temperatures via the so-called thermofield transformation [20][21][22][23] we refer the reader to Refs. [14,15] and references therein.…”

Section: Quantum Evolution Methodsmentioning

confidence: 99%

“…This geometry is suitable for tensor network methods due to the interactions being only of nearest-neighbor distance, but it suffers from larger entanglement. In this paper, we employ an improved chain mapping of the conduction electrons, with both short-range interactions and low entanglement [14]. The essential idea of the technique is a separation of electron modes above and below the bath chemical potential, followed by an independent chain mapping.…”

Section: Quantum Evolution Methodsmentioning

confidence: 99%

“…Since â1,n,σ and â2,n,σ are linear combinations of modes that are empty (filled) in the ground state, they are completely empty (filled) as well, and hence, the conduction electron bath ground state is a simple product state, which, as demonstrated in Refs. [14,15], is highly beneficial for the simulations. The final Hamiltonian to simulate consists of two Wilson's chains, and the impurity interacting with the first site of both chains:…”

Section: Quantum Evolution Methodsmentioning

confidence: 99%

“…At zero temperature, there is one more simplification possible. Instead of calculating the equilibrium state through a preliminary real-time annealing evolution [14], we can simply use the DMRG algorithm to calculate the ground state of the system variationally. Even if finite temperature simulations are possible as well [14], here we will for simplicity restrict ourselves to zero temperature, where the study of switching-time dependence is more directly addressed.…”

Section: Quantum Evolution Methodsmentioning

confidence: 99%

“…We address the fundamental quantum mechanical starting point of these questions by simulating the full real-time dynamics of the externally perturbed Anderson model of a quantum impurity, whose Kondo effect is switched with different means and time-dependencies. All results are obtained employing our recently established, state-of-the-art numerical technique based on matrix product states [14,15] . The remaining questions of experimental time scales, more qualitative, will be addressed in the discussion part.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Kondo nanomechanical dissipation in the driven Anderson impurity model

Kohn¹,

Santoro²,

Fabrizio³

et al. 2022

Preprint

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“…For more details and the extension to finite temperatures via the so-called thermofield transformation [20][21][22][23] we refer the reader to Refs. [14,15] and references therein.…”

Section: Quantum Evolution Methodsmentioning

confidence: 99%

Section: Quantum Evolution Methodsmentioning

confidence: 99%

Section: Quantum Evolution Methodsmentioning

confidence: 99%

Section: Quantum Evolution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Kondo nanomechanical dissipation in the driven Anderson impurity model

Kohn¹,

Santoro²,

Fabrizio³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Time-Dependent Density Matrix Renormalization Group Method for Quantum Transport with Phonon Coupling in Molecular Junction

Yang,

Li,

Ren

et al. 2023

J. Chem. Theory Comput.

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Quantum transport in molecular junctions has attracted great attention. The charge motion in a molecular junction can cause geometric deformation, leading to strong electron phonon coupling, which was often overlooked. We have formulated a nearly exact method to assess the time-dependent current and occupation number in the molecular junction modeled by the electron–phonon coupled bridge state using the time-dependent density matrix renormalization group (TD-DMRG) method. The oscillation period and amplitude of the current are found to be dependent on the electron phonon coupling strength and energy level alignment with the electrodes. In an attempt to better understand these phenomena, we have devised a new approximation that explains the bistability phenomenon and the behavior of steady currents in the strong electron–phonon coupling regime. Comparisons have been made with the multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method and the analytical result in the purely electronic limit. Furthermore, we explore the entropy of different orderings, extending to the electron phonon model problems. Regarding finite temperature, the thermal Bogoliubov transformation of both fermions and bosons is used and compared with imaginary time evolution results.

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MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics

Lacroix,

Le Dé,

Riva

et al. 2024

The Journal of Chemical Physics

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The MPSDynamics.jl package provides an easy-to-use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm based on environment chain mapping. The simulations rely on a tensor network representation of the quantum states as matrix product states (MPS) and tree tensor network states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle method for time evolution (including novel bond-adaptive one-site algorithms). The package also provides strong support for the measurement of single and multi-site observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. It currently handles long-range interactions, time-dependent Hamiltonians, multiple environments, bosonic and fermionic environments, and joint system–environment observables.

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Efficient mapping for Anderson impurity problems with matrix product states

Cited by 22 publications

References 59 publications

Kondo nanomechanical dissipation in the driven Anderson impurity model

Kondo nanomechanical dissipation in the driven Anderson impurity model

Time-Dependent Density Matrix Renormalization Group Method for Quantum Transport with Phonon Coupling in Molecular Junction

MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics

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