Entanglement structure of the Hubbard model in momentum space

Abstract

We study the properties of the ground states of the one- and two-dimensional Hubbard models at half filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix renormalization group (DMRG). In particular, we investigate quantities such as the single-site entropy and two-site mutual information of single-particle momentum states as well as the behavior of the bipartite subsystem entropy for partitions in momentum space. The distribution of these quantities in momentum space gives insight into the fundamental nature of the ground state, insight that can be used to make contact with weak-coupling-based analytic approaches and to optimize numerical methods, the momentum-space DMRG in particular. We study the site and subsystem entropies as a function of interaction strength $U$ and system size. In both the one- and two-dimensional cases, we find that the subsystem entropy scales proportionally to $U^2$ for weak $U$ and proportionally to volume. Nevertheless, the optimized momentum-space DMRG can provide variationally accurate results for the two-dimensional Hubbard model at weak coupling for moderate system sizes.

14 pages, 14 figures. In v3, the legends in Fig. 6 have been corrected

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• A class of quantum many-body states that can be efficiently simulated
• Area laws in quantum systems: mutual information and correlations
• New Trends in Density Matrix Renormalization
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Entanglement Measures for Single- and Multi-Reference Correlation Effects
• Resonating valence bond states in the PEPS formalism
• Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Investigation of metal-insulator like transition through the ab initio density matrix renormalization group approach
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices

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• Anisotropy crossover in the frustrated Hubbard model on four-chain cylinders
• General interaction quenches in a Luttinger liquid
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• Scaling up the transcorrelated density matrix renormalization group
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