Efficient quantum simulation for thermodynamics of infinite-size many-body

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.