Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0707.0142

Mott metal-insulator transition in the Hubbard model

Fusayoshi J. Ohkawa
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Hubbard model in the strong-coupling regime is mainly studied by Kondo-lattice theory or 1/d expansion theory, with d the spatial dimensionality. In two dimensions and higher, the ground state within the Hilbert subspace with no order parameter is a normal Fermi liquid except for n=1 and U/W=+infinity, with n the electron density per unit cell, U the on-site repulsion, and W the bandwidth; the cooperation between the Kondo effect, which favors a local singlet on each unit cell, and a resonating-valence-bond effect, which favors a local singlet on each pair of nearest-neighbor unit cells, stabilizes the Fermi liquid, whose ground state is a singlet as a whole, in the strong-coupling regime. In the whole Hilbert space with no restriction, the normal Fermi liquid is unstable at least against a magnetic or superconducting state. This analysis confirms an early Fermi-liquid theory of high-temperature superconductivity, F. J. Ohkawa, Jpn. J. Appl. Phys. 26, L652 (1987). The ground state for n=1 and U/W=+infinity is a Mott insulator. Actual metal-insulator transitions cannot be explained within the Hubbard model. In order to explain them, the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model. The crossover between local-moment magnetism and itinerant-electron magnetism corresponds to that between a localized spin and a normal Fermi liquid in the Kondo effect and it is simply a Mott metal-insulator crossover.

Explore related subjects

cond-mat.str-elcond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Fusayoshi J. Ohkawa. 2007-07-02. Mott metal-insulator transition in the Hubbard model. https://arxiv.org/abs/0707.0142

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Tensor Network Representations for Intrinsically Mixed-State Topological Orders

Tensor networks are an efficient platform for representing topological states of matter as well as computing both physical observables and information-theoretic quantities. We present a general protocol to construct tensor network representations for intrinsically mixed-state topological phases. Such phases naturally emerge in noisy long-range entangled quantum systems, and exhibit nontrivial topological phenomena without pure-state counterparts. The method exploits the isomorphism between anyon decoherence in the physical Hilbert space and anyon condensation in the corresponding Choi space. The protocol is applicable to a broad class of systems arising from decoherence of pure-state topological phases, where the incoherent noise creates excitations in the Choi space that have trivial monodromy with all excitations. Representative examples at renormalization group fixed points include $m^a e^b$ decoherence in the $\Z_N$ toric code, decohered non-Abelian quantum double of $S_3$ as well as pure $Z$/$X$ decoherence of arbitrary CSS codes. Another notable example is that of the mixed-state chiral semion, whose tensor network representation has no pure-state analogue. We then generalize the formalism beyond RG fixed points and, as an example, examine the decoherence transition in a $\mathbb{Z}_3$ toric code channel that suffers from sign problem when mapped to a statistical mechanical model. Together, these results establish tensor networks as a natural platform for analyzing noisy intrinsically mixed-state topological matter.

cond-mat.str-el↗
arXiv2026

Frustration from Localized Zhang-Rice States: A Unified Theory of Doping-Driven Magnetic Transitions in Cuprates

The microscopic mechanism by which doped holes disrupt the antiferromagnetic (AFM) order is one of the fundamental questions in cuprates. In this work, we propose a unified microscopic theory in which doped holes form spatially localized Zhang-Rice singlets which actively mediate emergent spin exchange. Rather than acting as simple non-magnetic vacancies, these localized states introduce emergent next-nearest $J_2$ and third-nearest $J_3$ neighbor superexchanges. This dopant-induced exchange pathway generates significant magnetic frustration, naturally explaining the rapid collapse of the Néel AFM order and the emergence of a spin-glass phase on the hole-doped side. In contrast, electron doping primarily leads to spin dilution, allowing AFM order to persist to substantially higher doping levels, consistent with the experimentally observed electron-hole asymmetry. Our findings provide a unified microscopic framework for understanding doping-driven magnetic transitions in lightly doped cuprates.

cond-mat.str-el↗
arXiv2026

Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor

We study an effective model of regular quantum dot clusters coupled to a common superconductor. By applying a canonical transformation, we map the system onto a particle-number-conserving representation, enabling an efficient treatment with standard fermionic neural-network quantum-state variational Monte Carlo methods. We show that the excitation gap can close under a particular high-symmetry condition, which, in finite non-interacting systems, corresponds to crossings between singlet ground states of different character. At this high-symmetry condition the model can be mapped to a standard Hubbard model in grand-canonical ensemble with fixed chemical potential away from half-filling. Combining exact methods, density matrix renormalization group, and neural quantum-state variational Monte Carlo calculations, we identify three distinct interacting regimes: a trivial superconducting singlet phase, a strongly correlated regime related to an effective Heisenberg model, and a critical intermediate regime with qualitatively different behavior in one and two dimensions. In one-dimensional systems, the intermediate regime exhibits a sequence of singlet-doublet transitions and becomes gapless in the thermodynamic limit even for finite Coulomb interaction. In two-dimensional clusters, we find robust triplet ground states. These results connect the physics of superconducting nanostructures with correlated lattice models and show that standard fermionic neural quantum states can capture the relevant interacting regimes.

cond-mat.str-el↗