Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions

By Z. Gu, Michael Levin, X. Wen. 2008

175 citations recorded by the source corpus.

Traditional mean-field theory is a generic variational approach for analyzing symmetry breaking phases. However, this simple approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for studying two-dimensional (2D) quantum phases with long-range entanglement (such as topological phases). The method is based on (a) a general class of trial wave functions known as tensor-product states and (b) a 2D real-space renormalization group algorithm for efficiently calculating expectation values for these states. We demonstrate our method by studying several simple 2D quantum spin models exhibiting both symmetry breaking phase transitions and topological phase transitions. Our approach can be viewed as a unified mean-field theory for both symmetry breaking phases and topological phases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/fcd6c5a939a31ae40bedf37e4c8f75418e991bcd

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

The ITensor Software Library for Tensor Network Calculations (2020, methodology): “Each step of TRG essentially consists of contracting four tensors together into a single tensor, then performing a truncated factorization of that tensor.”
Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, methodology): “|DS〉 admits an exact tensor-network representations [35, 36] (see Fig.”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “In (Gu et al., 2008; Gu and Wen, 2009), it was realized that the local symmetries of the tensors are of primordial importance for describing long range topological order, and in (Schuch et al., 2011) this was formalized by the crucial concept of Ginjectivity and later by the more general concept of…”
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems (2014, unknown): “[75], which quickly led to accurate results.”