scholarly journals Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160431 ◽  
Author(s):  
Trithep Devakul ◽  
Vedika Khemani ◽  
Frank Pollmann ◽  
David A. Huse ◽  
S. L. Sondhi
Keyword(s):  
Quantum Systems ◽  
Exact Diagonalization ◽  
Density Matrix Renormalization Group ◽  
Exact Results ◽  
Free Fermion ◽  
Many Body ◽  
Spin Models ◽  
Actual Performance ◽  
Density Matrix Renormalization ◽  
Xx Model

We benchmark a variant of the recently introduced density matrix renormalization group (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. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

scholarly journals Many-Body Effects in FeN4 Center Embedded in Graphene

2020 ◽  
Vol 10 (7) ◽  
pp. 2542 ◽  
Author(s):  
Andrew Allerdt ◽  
Hasnain Hafiz ◽  
Bernardo Barbiellini ◽  
Arun Bansil ◽  
Adrian E. Feiguin
Keyword(s):  
Transition Metal Complexes ◽  
First Principles ◽  
Density Functional ◽  
Coulomb Repulsion ◽  
Density Matrix Renormalization Group ◽  
Orbital Interaction ◽  
Many Body ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Density Matrix Renormalization

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.

scholarly journals Shift-invert diagonalization of large many-body localizing spin chains

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Francesca Pietracaprina ◽  
Nicolas Macé ◽  
David J. Luitz ◽  
Fabien Alet
Keyword(s):  
Random Field ◽  
Linear Algebra ◽  
Spin Chain ◽  
Quantum Systems ◽  
Exact Diagonalization ◽  
Spin Chains ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Sparse Linear Algebra

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to L=26L=26. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

EXACT RESULTS FOR MANY-BODY PROBLEMS USING FEW-BODY METHODS

2006 ◽  
Vol 20 (19) ◽  
pp. 2595-2602
Author(s):  
JOHN CARDY
Keyword(s):  
Recent Progress ◽  
Quantum Systems ◽  
Point Of View ◽  
Exact Results ◽  
Many Body ◽  
New Approach ◽  
One Dimensional ◽  
Many Body Theory ◽  
Loewner Evolution ◽  
Body Theory

Recently there has been developed a new approach to the study of critical quantum systems in 1+1 dimensions which reduces them to problems in one-dimensional Brownian motion. This goes under the name of stochastic, or Schramm, Loewner Evolution (SLE). I review some of the recent progress in this area, from the point of view of many-body theory. Connections to random matrices also emerge.

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