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  • Letter

Non-Markovian stochastic Schrödinger equation: Matrix-product-state approach to the hierarchy of pure states

Xing Gao1,*, Jiajun Ren2,†, Alexander Eisfeld3, and Zhigang Shuai2

  • 1School of Materials, Sun Yat-sen University, Shenzhen, Guangdong 518107, China
  • 2MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, China
  • 3Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany

  • *gxing@mail.sysu.edu.cn
  • †jiajunren0522@gmail.com
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Phys. Rev. A 105, L030202 – Published 31 March, 2022

DOI: https://doi.org/10.1103/PhysRevA.105.L030202

Abstract

We derive a stochastic hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in an open quantum system at finite temperature, which is numerically exact and efficient. HOMPS is obtained from the recently developed stochastic hierarchy of pure states (HOPS) by expressing HOPS in terms of formal creation and annihilation operators. The resulting stochastic first-order differential equation is then formulated in terms of matrix product states and matrix product operators. In this way the exponential complexity of HOPS can be reduced to scale polynomial with the number of particles. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.

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Phys. Rev. A 105, L030202– Published 31 March, 2022
  • Received 20 September 2021
  • Accepted 17 March 2022
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