1. Obtaining highly excited eigenstates of the localized XX chain via DMRG-X
- Author
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David A. Huse, Vedika Khemani, Trithep Devakul, Frank Pollmann, and Shivaji Lal Sondhi
- Subjects
Superconductivity and magnetism ,Physics ,Quantum Physics ,Random field ,Statistical Mechanics (cond-mat.stat-mech) ,General Mathematics ,Density matrix renormalization group ,General Engineering ,FOS: Physical sciences ,General Physics and Astronomy ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Articles ,Condensed Matter - Disordered Systems and Neural Networks ,01 natural sciences ,010305 fluids & plasmas ,Exact results ,Chain (algebraic topology) ,Quantum mechanics ,Excited state ,0103 physical sciences ,Benchmark (computing) ,Quantum Physics (quant-ph) ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Eigenvalues and eigenvectors - Abstract
We benchmark a variant of the recently introduced DMRG-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many body localized spin models near a transition., Updated ver
- Published
- 2017