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

2008/06/23 by Zheng‐Cheng Gu, Zheng-Cheng Gu, Michael Levin +1 · 16 citations
Mathematics · Physics and Astronomy · #Density matrix renormalization group #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization group #Spontaneous symmetry breaking #Symmetry breaking #Symmetry protected topological order #Tensor (intrinsic definition) #Tensor product #Theoretical physics #Topological order #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.78.205116

published as Phys. Rev. B 78, 205116 (2008) · 4 pages, RevTeX4

arxiv created 2008/06/23 · openalex publication_date 2008/11/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Criticality, the area law, and the computational power of PEPS
• Fermions without Fermion Fields
• String-net condensation: A physical mechanism for topological phases
• An introduction to lattice gauge theory and spin systems
• Fault-tolerant quantum computation by anyons
• Quantum orders and symmetric spin liquids

Cited by

• Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
• Perturbative 2-body parent Hamiltonians for projected entangled pair states
• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Density of States of Quantum Spin Systems from Isotropic Entanglement
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states
• The structure of fixed-point tensor network states characterizes the patterns of long-range entanglement
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Spin-one bilinear-biquadratic model on a star lattice
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• Controlling sign problems in spin models using tensor renormalization
• Ground-state properties of quantum many-body systems: entangled-plaquette states and variational Monte Carlo
• Disentangling theorem and monogamy for entanglement negativity
• Variational Monte Carlo simulations using tensor-product projected states
• Tree tensor networks and entanglement spectra
• Tensor network analysis of critical coupling in two dimensional ϕ4 theory

Related

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Tensor-product representations for string-net condensed states
• Identifying two-dimensional topological phase transition by entanglement spectrum : A fermion Monte Carlo study
• Modified Tucker Decomposition for Tensor Network and Fast Linearized Tensor Renormalization Group Algorithm for Two-Dimensional Quantum Spin Lattice Systems