Making trotters sprint: A variational imaginary time ansatz for quantum many-body systems

Matthew J. S. Beach, Roger G. Melko, Tarun Grover, and Timothy H. Hsieh
Phys. Rev. B 100, 094434 – Published 20 September 2019
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Abstract

We introduce a variational wave function for many-body ground states that involves imaginary-time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. We successfully apply the ansatz on the one- and two-dimensional transverse-field Ising model and systematically study its scaling for the one-dimensional model at criticality. We find the total imaginary time required scales logarithmically with system size, in contrast to the linear scaling in conventional quantum Monte Carlo. We suggest this is due to unique dynamics permitted by alternating imaginary-time evolution, including exponential growth of bipartite entanglement. For generic models, the superior scaling of our ansatz potentially mitigates the negative sign problem at the expense of having to optimize variational parameters.

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  • Received 10 April 2019
  • Revised 25 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.094434

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matthew J. S. Beach1,2, Roger G. Melko1,2, Tarun Grover3, and Timothy H. Hsieh1

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
  • 2Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 3Department of Physics, University of California at San Diego, La Jolla, California 92093, USA

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Issue

Vol. 100, Iss. 9 — 1 September 2019

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