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Published September 7, 2024 | Published
Journal Article Embargoed

Correlation functions from tensor network influence functionals: The case of the spin-boson model

Nguyen, Haimi1 ORCID icon
Ng, Nathan1 ORCID icon
Lindoy, Lachlan P.2 ORCID icon
Park, Gunhee3 ORCID icon
Millis, Andrew J.1, 4 ORCID icon
Kin-Lic Chan, Garnet3 ORCID icon
Reichman, David R.1 ORCID icon
  • 1. ROR icon Columbia University
  • 2. ROR icon National Physical Laboratory
  • 3. ROR icon California Institute of Technology
  • 4. Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA

Abstract

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff–Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Copyright and License

© 2024 Author(s). Published under an exclusive license by AIP Publishing.

Acknowledgement

This work was performed with support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program, under Award No. DE-SC0022088. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231. The Flatiron Institute is a division of the Simons Foundation. L.P.L. acknowledges the support of the Engineering and Physical Sciences Research Council (Grant No. EP/Y005090/1). G.K.-L.C. is a Simons Investigator in Physics.

Contributions

Haimi Nguyen: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Nathan Ng: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Lachlan P. Lindoy: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Gunhee Park: Conceptualization (equal); Writing – review & editing (equal). Andrew J. Millis: Conceptualization (equal); Funding acquisition (equal); Supervision (supporting); Writing – review & editing (equal). Garnet Kin-Lic Chan: Conceptualization (equal); Funding acquisition (equal); Supervision (supporting); Writing – review & editing (equal). David R. Reichman: Conceptualization (equal); Funding acquisition (equal); Project administration (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal).

Data Availability

The data that support the findings of this study are available upon reasonable request. The code is available on Github at https://github.com/nguye66h/sb-ecfs.

Supplemental Material

See the supplementary material for (1) more data on the convergence behavior of the thermal correlation function on the KB contour and the steady state correlation function; (2) explicit expressions for the ηk,k′ and system propagators on the KB and CT contours; and (3) details of the ML-MCTDH approach used for evaluating symmetrized and equilibrium correlation functions.

Additional Information

This paper is part of the JCP Special Topic on Algorithms and Software for Open Quantum System Dynamics

Files

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Embargoed

The files will be made publicly available on September 7, 2025.

Reason: Publisher requires 12-month embargo

Additional details

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October 11, 2024
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October 11, 2024