Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

Abstract

The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to two-dimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.

33 pages, 18 figures; corrected Eq.(117)

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Cited by in corpus (28)

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• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• The Density Matrix Renormalization Group for finite Fermi systems
• Fractional Quantum Hall Effects in Graphene and Its Bilayer
• Ground State of v=1 Bilayer Quantum Hall Systems
• Density Matrix Renormalization Group and the Nuclear Shell Model
• Coupled charge and valley excitations in graphene quantum Hall ferromagnets
• Electron-phonon coupling and spin-charge separation in one-dimensional Mott insulators
• Accurate computation of low-temperature thermodynamics for quantum spin chains
• Topological entropy of realistic quantum Hall wave functions
• Trapping Abelian anyons in fractional quantum Hall droplets
• Stripe State in the Lowest Landau Level
• Domain Formation in v=2/3 Fractional Quantum Hall Systems
• Coherent-Incoherent Crossover of Charge and Neutral Mode Transport as Evidence for the Disorder-Dominated Fractional Edge Phase
• Real Space Effective Interaction and Phase Transition in the Lowest Landau Level
• Density matrix renormalization group study of the $\nu =1/3$ edge states in fractional quantum Hall systems
• Entanglement Entropy of Random Fractional Quantum Hall Systems
• Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit
• Spin-Orbit Interaction Enhanced Fractional Quantum Hall States in the Second Landau Level
• U(1) symmetry breaking in one-dimensional Mott insulator studied by the Density Matrix Renormalization Group method
• Magnetization-based assessment of correlation energy in canted Single-Chain Magnets
• Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure
• Phase diagram of a frustrated asymmetric ferromagnetic spin ladder
• Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets
• Entropic Quantum Machine