Valence Bond Entanglement and Fluctuations in Random Singlet Phases

Abstract

The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain can be viewed as a strongly fluctuating liquid of valence bonds, while in disordered chains these bonds lock into random singlet states on long length scales. We show that this phenomenon can be studied numerically, even in the case of weak disorder, by calculating the mean value of the number of valence bonds leaving a block of $L$ contiguous spins (the valence-bond entanglement entropy) as well as the fluctuations in this number. These fluctuations show a clear crossover from a small $L$ regime, in which they behave similar to those of the uniform model, to a large $L$ regime in which they saturate in a way consistent with the formation of a random singlet state on long length scales. A scaling analysis of these fluctuations is used to study the dependence on disorder strength of the length scale characterizing the crossover between these two regimes. Results are obtained for a class of models which include, in addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical 1D transverse-field Ising model and chains of interacting non-Abelian anyons.

8 pages, 6 figures

References in corpus (6)

• Interacting anyons in topological quantum liquids: The golden chain
• Valence Bond Entanglement Entropy
• Correlation amplitude and entanglement entropy in random spin chains
• Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
• Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains
• Monte Carlo Simulations of Interacting Anyon Chains

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• Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain
• Entanglement entropy and localization in disordered quantum chains
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Fibonacci sequence and its generalizations in doped quantum spin ladders