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Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

Journal Article · · Physical Review. B
 [1];  [2]
  1. Philipps-Universität Marburg (Germany)
  2. Philipps-Universität Marburg (Germany); MTA Wigner Research Centre for Physics, Budapest (Hungary); Technical University of Munich, Garching (Germany)
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Here we apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction U equals the bandwidth Uc = W, where the single-particle gap opens linearly, Δ(U ≥ W) = U - W. The simple nature of the elementary excitations permits us to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $$n_k$$ at the Fermi wave number $$k_F$$ = 0 cannot be used to locate accurately Uc from finite-size systems. However, the slope of $$n_k$$ at the band edges $$k_B$$ = ±π, reveals the formation of a single-particle bound state which can be used to determine Uc reliably from $$n_k$$ using accurate finite-size data.
Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
Alexander von Humboldt Foundation; Hungarian National Research, Development and Innovation Office (NKFIH); Hungarian Quantum Technology National Excellence Program; Quantum Information National Laboratory of Hungary; Technical University of Munich; USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division (CSGB)
Grant/Contract Number:
AC05-76RL01830
OSTI ID:
1982770
Alternate ID(s):
OSTI ID: 1835461
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 24 Vol. 104; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

1-dimensional systems
36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Hubbard model
density matrix renormalization group
metal-insulator