Real-time evolution of Anderson impurity models via tensor network influence functionals

Ng, Nathan; Park, Gunhee; Millis, Andrew J.; Chan, Garnet Kin‐Lic; Reichman, David R.

doi:10.1103/physrevb.107.125103

Cited by 28 publications

(3 citation statements)

References 61 publications

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“…Throughout this work we will consider a semicircular spectrum (this type of spectrum was also considered in, e.g. [22,39,44,45])…”

Section: Grassmann Pi On the Imaginary-time Axismentioning

confidence: 99%

“…In the last five years, important progress has been made in tensor-network-based impurity solvers by using the Feynman-Vernon influence functional (IF) [29] to integrate out the bath analytically, which avoids explicitly treatment on the bath. This idea has been first implemented in bosonic systems under the name of the time-evolving matrix product operators (TEMPO) [30], which has achieved unprecedented accuracy and efficiency in studying the non-equilibrium dynamics for bosonic impurity problems [31][32][33][34][35][36], and then in fermionic systems [37][38][39][40] (the latter methods will be referred to as the tensor network IF methods in the following). In our previous work, we propose a Grassmann time-evolving matrix product operator (GTEMPO) method which is a full fermionic analog of the TEMPO method [41].…”

Section: Introductionmentioning

confidence: 99%

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Grassmann time-evolving matrix product operators for equilibrium quantum impurity problems

Chen,

Xu,

Guo

2024

New J. Phys.

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Tensor-network-based methods are promising candidates to solve quantum impurity problems. They are free of sampling noises and the sign problem compared to state-of-the-art continuous-time quantum Monte Carlo methods. Recent progress made in tensor-network-based impurity solvers is to use the Feynman-Vernon influence functional to integrate out the bath analytically, retaining only the impurity dynamics and representing it compactly as a matrix product state. The recently proposed Grassmann time-evolving matrix product operator (GTEMPO) method is one of the representative methods in this direction.In this work, we systematically study the performance of GTEMPO in solving equilibrium quantum impurity problems at a finite temperature with a semicircular spectrum density of the bath. Our results show that its computational cost would generally increase as the temperature goes down and scale exponentially with the number of orbitals. In particular, the single-orbital Anderson impurity model can be efficiently solved with this method, for two orbitals we estimate that one could possibly reach inverse temperature $\beta\approx 20$ if high-performance computing techniques are utilized, while beyond that only very high-temperature regimes can be reached in the current formalism. Our work paves the way to apply GTEMPO as an imaginary-time impurity solver.

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“…Throughout this work we will consider a semicircular spectrum (this type of spectrum was also considered in, e.g. [22,39,44,45])…”

Section: Grassmann Pi On the Imaginary-time Axismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Grassmann time-evolving matrix product operators for equilibrium quantum impurity problems

Chen,

Xu,

Guo

2024

New J. Phys.

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“…Given the cavity GF, we construct an exact hybridization self-energy for the embedded impurity: normalΔ </> ( ε ) = ∑ i , j ∈ N 0 t i 0 t j 0 * [ G cavity </> false( ε false) ] i j This fully describes the effect of the bath on the impurity GF, and the calculation of G imp takes the form of a standard quantum impurity problem, albeit with an intrinsically nonequilibrium bath action. Different approximations and numerically exact methods could solve this problem, ,− but relatively few are capable of producing reliable results in the strongly correlated nonequilibrium regime in which we are interested (see the Supporting Information). We employ the recently developed steady-state inchworm quantum Monte Carlo method .…”

Section: The Systemmentioning

confidence: 99%

Shaping Electronic Flows with Strongly Correlated Physics

Erpenbeck,

Gull,

Cohen

2023

Nano Lett.

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Nonequilibrium quantum transport is of central importance in nanotechnology. Its description requires the understanding of strong electronic correlations that couple atomic-scale phenomena to the nanoscale. So far, research in correlated transport has focused predominantly on few-channel transport, precluding the investigation of cross-scale effects. Recent theoretical advances enable the solution of models that capture the interplay between quantum correlations and confinement beyond a few channels. This problem is the focus of this study. We consider an atomic impurity embedded in a metallic nanosheet spanning two leads, showing that transport is significantly altered by tuning only the phase of a single local hopping parameter. Furthermore�depending on this phase� correlations reshape the electronic flow throughout the sheet, either funneling it through the impurity or scattering it away from a much larger region. This demonstrates the potential for quantum correlations to bridge length scales in the design of nanoelectronic devices and sensors.

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Improved memory truncation scheme for quasi-adiabatic propagator path integral via influence functional renormalization

Liu,

Ren,

Fang

2024

The Journal of Chemical Physics

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Accurately simulating non-Markovian quantum dynamics in system–bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time.

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Real-time evolution of Anderson impurity models via tensor network influence functionals

Cited by 28 publications

References 61 publications

Grassmann time-evolving matrix product operators for equilibrium quantum impurity problems

Grassmann time-evolving matrix product operators for equilibrium quantum impurity problems

Shaping Electronic Flows with Strongly Correlated Physics

Improved memory truncation scheme for quasi-adiabatic propagator path integral via influence functional renormalization

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