Tensor network approaches for higher-dimensional quantum lattice models

Abstract

In this section, we will show several representative TN approaches for simulating the quantum lattice models in (d > 1) dimensions. We will mainly use the language of TN contractions. One may refer to several existing reviews (Schollwöck, Ann Phys 326:96–192, 2011; Verstraete et al., Adv Phys 57:143–224, 2008; Cirac and Verstraete, J Phys A Math Theor 42:504004, 2009; Orús, Ann Phys 349:117, 2014; Haegeman and Verstraete, Ann Rev Condens Matter Phys 8(1):355–406, 2017) for more exhaustive understanding on the TN simulations for quantum problems. We will focus on the algorithms based on PEPS, and show the key roles that the 2D TN contraction algorithms presented in Sect. 3 play in the higher-dimensional cases.