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Studying Two Dimensional Systems With the Density Matrix Renormalization Group

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arxiv 1105.1374 v2 pith:ALG6M56D submitted 2011-05-06 cond-mat.str-el cond-mat.supr-con

E.M. Stoudenmire , Steven R. White This is my paper · ORCID
classification cond-mat.str-elcond-mat.supr-con
keywords dmrgdensitygroupmatrixmethodmethodsremainsrenormalization
verification ladder T0 review T1 audit T2 compute T3 formal
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The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past applications of DMRG in 2D demonstrates its success in treating a wide variety of problems, although it remains underutilized in this setting. We present techniques for performing cutting edge 2D DMRG studies including methods for ensuring convergence, extrapolating finite-size data and extracting gaps and excited states. Finally, we compare the current performance of a recently developed tensor network method to 2D DMRG.

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Cited by 3 Pith papers

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  1. A Finite-Volume Scheme for the Continuum Extrapolation of Lattice Step-Scaling in (2+1)D Hamiltonian U(1) Gauge Theory

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    Introduces and tests a finite-volume scheme enabling stable continuum extrapolation of the step-scaling function in (2+1)D Hamiltonian U(1) gauge theory via matrix product states.

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    For the doped square-lattice Hubbard model, hidden-fermion and backflow neural quantum states with a Vision Transformer backbone reach nearly equal variational energies; translation-equivariant attention is outperform...

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    quant-ph 2025-06 conditional novelty 4.0 of 10

    IQPE with a single Slater determinant reproduces exact ground-state energies for the Hubbard model on a six-site graphene hexagon in noiseless simulation, while hardware noise limits accuracy on current IBM devices.

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