Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study

Abstract

Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly $c$, the sound velocity $v_s$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_s$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_A,S)$ of the spin-$S$ Heisenberg chains satisfies the relation $S(L,l_A,S)-S(L,l_A,S-1)=1/(2S+1)$ for $S>3/2$ in the thermodynamic limit.

7 pages, 3 figs., 3 tables, to appear in PRB. Added new results for s>1/2

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• Entanglement entropy of two disjoint intervals in c=1 theories
• Tomonaga-Luttinger-liquid criticality: numerical entanglement entropy approach
• The entanglement entropy of 1D systems in continuous and homogenous space
• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Conformal fields and operator product expansion in critical quantum spin chains
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Quantum phase transitions in multileg spin ladders with ring exchange
• Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field
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• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
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• Universal Finite-Size Corrections of the Entanglement Entropy of Quantum Ladders and the Entropic Area Law
• Phase diagram of 1+1D Abelian-Higgs model and its critical point
• Spectral properties of critical 1+1D Abelian-Higgs model