Efficient quantum simulation for thermodynamics of infinite-size many-body systems in arbitrary dimensions

Shi-Ju Ran1,2,*Bin Xi3Cheng Peng4Gang Su4,5, and Maciej Lewenstein2,6

  • 1Department of Physics, Capital Normal University, Beijing 100048, China
  • 2ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
  • 3College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China
  • 4School of Physical Sciences, University of Chinese Academy of Sciences, P. O. Box 4588, Beijing 100049, China
  • 5Kavli Institute for Theoretical Sciences and CAS Center for Excellence in Topological Quantum Computation
  • 6ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
  • *Corresponding author: sjran@cnu.edu.c


    In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show that the QES can, for instance, accurately simulate varieties of many-body phenomena, including finite-temperature crossover and algebraic excitations of the one-dimensional spin liquid, the phase transitions and low-temperature physics of the two- and three-dimensional antiferromagnets, and the crossovers of the two-dimensional topological system. Our work provides an efficient way to explore the thermodynamics of intractable quantum many-body systems with easily accessible systems.