Efficient quantum simulation for thermodynamics of infinite-size many-body systems in arbitrary dimensions
Shi-Ju Ran,^1,2,* Bin Xi,³ Cheng Peng,⁴ Gang Su,^4,5 and Maciej Lewenstein ^2,6
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
(Received 30 November 2018; revised manuscript received 4 May 2019; published 20 May 2019)

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 threedimensional 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.