Tensor Network Annealing Algorithm for Two-Dimensional Thermal States

A. Kshetrimayum, M. Rizzi, J. Eisert, and R. Orús
Phys. Rev. Lett. 122, 070502 – Published 22 February 2019

Abstract

Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark, we study the finite-temperature phase transition of the Ising model on an infinite square lattice, for which we obtain remarkable agreement with the exact solution. We then turn to study the finite-temperature Bose-Hubbard model in the limits of two (hard-core) and three bosonic modes per site. Our technique can be used to support the experimental study of actual effectively two-dimensional materials in the laboratory, as well as to benchmark optical lattice quantum simulators with ultracold atoms.

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  • Received 10 October 2018
  • Revised 18 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.070502

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

A. Kshetrimayum1,2, M. Rizzi2, J. Eisert1,3, and R. Orús2,4,5

  • 1Dahlem Center for Complex Quantum Systems, Physics Department, Freie Universität Berlin, 14195 Berlin, Germany
  • 2Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany
  • 3Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
  • 4Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
  • 5Ikerbasque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain

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Issue

Vol. 122, Iss. 7 — 22 February 2019

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