Density-Matrix Renormalization-Group Analysis of Quantum Critical Points: I. Quantum Spin Chains

Abstract

We present a simple method, combining the density-matrix renormalization-group (DMRG) algorithm with finite-size scaling, which permits the study of critical behavior in quantum spin chains. Spin moments and dimerization are induced by boundary conditions at the chain ends and these exhibit power-law decay at critical points. Results are presented for the spin-1/2 Heisenberg antiferromagnet; an analytic calculation shows that logarithmic corrections to scaling can sometimes be avoided. We also examine the spin-1 chain at the critical point separating the Haldane gap and dimerized phases. Exponents for the dimer-dimer and the spin-spin correlation functions are consistent with results obtained from bosonization.

21 pages, 12 figures, new results and added references, to appear in PRB

References in corpus (2)

• Heisenberg Spin-One Chain in Staggered Magnetic Field : A Density Matrix Renormalization Group Study
• Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation

Cited by in corpus (19)

• The density-matrix renormalization group
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• New Trends in Density Matrix Renormalization
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Friedel Oscillations and Charge Density Waves in Chains and Ladders
• Entanglement entropy in quantum impurity systems and systems with boundaries
• Scaling of the entanglement spectrum near quantum phase transitions
• Quantum Impurity Entanglement
• Magnetization and dimerization profiles of the cut two-leg spin ladder and spin-1 chain
• Staggered Flux Phase in a Model of Strongly Correlated Electrons
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods
• Emergent quasi-one-dimensionality in a kagomé magnet: A simple route to complexity
• Truncation effects in the charge representation of the O(2) model
• Critical Entanglement for the Half-Filled Extended Hubbard Model
• Orbital currents and charge density waves in a generalized Hubbard ladder
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Antiferromagnetic integer-spin chains in a staggered magnetic field: approaching the thermodynamic limit through the infinite-size DMRG
• Metric response of relative entropy: A universal indicator of quantum criticality