Schmidt gap and quantum phase transitions in the XXZ model under external field on the Bethe lattice

¹ Department of Physics, Tianjin Polytechnic University - Tianjin 300387, China
² Department of Physics, Beihang University - Beijing, 100191, China
³ School of Physical Science and Technology, Soochow University - Suzhou, Jiangsu 215006, China
⁴ Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, College of Physical Sciences, Graduate University of Chinese Academy of Sciences P. O. Box 4588, Beijing 100049, China
⁵ School of Physics, Peking University - Beijing 100871, China

Received: 3 January 2013
Accepted: 12 February 2013

Abstract

Along the line developed in a recent paper by one of the authors (Li W., von Delft J. and Xiang T., Phys. Rev. B, 86 (2012) 195137), a simple update scheme, as an optimal method for optimizing the infinite tree tensor network (iTTN) states, is utilized to study the XXZ model under external field on the Bethe lattice. The ground-state energy, bipartite entanglement, order parameters, and nearest-neighbor correlation functions are calculated in the framework of the iTTN states. With increasing external field, two quantum phase transitions (QPTs) (a first-order and a second-order one) take place successively. Between the antiferromagnetic phase and the saturated ferromagnetic phase, there exists another intermediate (canted Néel) phase, in which both x-axis antiferromagnetic order and unsaturated z-axis ferromagnetic order coexist. An interesting spin-flop transition between antiferromagnetic phase and canted Néel phase is observed. The model-independent bipartite entanglement is found to be capable of describing all the QPTs. It is interesting that the Schmidt gap acts as a local order parameter, and can also be used to describe the QPTs.