Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2201.05432 · Physical review. B./Physical review. B

Doped Mott insulator on a Penrose tiling

志朗 酒井, Nayuta Takemori

Published May 27, 2022• 9 citations
arXivHTMLPDF

Abstract

We study the effect of carrier doping to the Mott insulator on the Penrose tiling, aiming at clarifying the interplay between quasiperiodicity and strong electron correlations. We numerically solve the Hubbard model on the Penrose-tiling structure within a real-space dynamical mean-field theory, which can deal with a spatial inhomogeneity as well as a singular self-energy necessary to describe the Mott insulator. We find that the strong correlation effect produces a charge distribution unreachable by a static mean-field approximation. In a small doping region, the spectrum shows a site-dependent gap just above the Fermi energy, which is generated by a singularly large self-energy emergent from the Mott physics and regarded as a real-space counterpart of the momentum-dependent pseudogap observed in a square-lattice Hubbard model.

DOI
10.1103/physrevb.105.205138

Related papers

Local Electron Correlations in a Two-Dimensional Hubbard Model on the Penrose Lattice

Nayuta Takemori, Akihisa Koga

We study electron correlations in the half-filled Hubbard model on two-dimensional Penrose lattice. Applying the real-space dynamical mean-field theory to large clusters, we discuss how low-temperature properties are affected by the quasiperiodic structure. By calculating the double occupancy and renormalization factor at each site, we clarify the existence of the Mott transition. The spatially-dependent renormalization characteristic of geometrical structure is also addressed.

arXiv:1411.7067•Journal of the Physical Society of Japan•Dec 25, 2014•34 citations

Pseudogap induced by short-range spin correlations in a doped Mott insulator

Bumsoo Kyung, S. S. Kancharla, David Sénéchal +3 more

We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the cellular dynamical mean-field theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum-dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.

arXiv:cond-mat/0502565•Physical Review B•Apr 13, 2006•269 citations

Nonperturbative approach to full Mott behavior

Tudor D. Stanescu, Philip Phillips

Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale ${t}^{2}/U)$ is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level $x<1/3.$ The sign change is tied to a termination of strong correlation physics in the doped Mott state.

arXiv:cond-mat/0301254•Physical Review B•Jun 15, 2004•38 citations

Pseudogaps in strongly correlated metals: A generalized dynamical mean-field theory approach

Michael V. Sadovskii, I. A. Nekrasov, É. Z. Kuchinskiǐ +2 more

We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ ($U$---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.

arXiv:cond-mat/0508585•Physical Review B•Oct 6, 2005•140 citations

Slave fermion interpretation of the pseudogap in doped Mott insulators

Zhuoqing Long, Jiangfan Wang, Yi‐feng Yang

We apply the recently developed slave fermion approach to study the doped Mott insulator in the one-band Hubbard and Hubbard-Heisenberg models. Our results produce several subtle features in the electron spectra and confirm the key role of antiferromagnetic (AFM) correlations in the appearance of the pseudogap. Upon hole doping, the electron spectra exhibit a single peak near the Fermi energy in the local approximation of the Hubbard model where AFM correlations are not included. When AFM correlations are included through an explicit mean-field Heisenberg interaction, a second peak emerges at slightly lower energy and pushes the other peak to higher energy, so that a pseudogap emerges between the two peaks at small doping. Both peaks grow rapidly with increasing doping and eventually merge together, where the pseudogap no longer exists. Detailed analyses of the spectral evolution with doping and the strength of the Heisenberg interaction confirm that the lower-energy peak comes from a polaronic mechanism due to the holon-spinon interaction in the AFM-correlated background and the higher-energy peak arises from the holon hybridization to form the electron quasiparticles. Thus, the pseudogap arises from the interplay of the polaronic and hybridization mechanisms. Our results are in good agreement with previous numerical calculations using the dynamical mean-field theory and its cluster extensions, but give a clearer picture of the underlying physics. Our work provides a promising perspective for clarifying the nature of doped Mott insulators and may serve as a starting point for more elaborate investigations in the future.

arXiv:2302.04620•Physical review. B./Physical review. B•Oct 17, 2023•4 citations

Interplay between the Pseudogap and Superconductivity in Doped Mott Insulators: a Cluster Dynamical Mean-Field Theory Study

Jinbin 晋斌 Liu 刘, Dao‐Xin Yao, Wéi Wú

Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.

Chinese Physics Letters•Jul 7, 2025•4 citations
We study the effect of carrier doping to the Mott insulator on the Penrose tiling, aiming at clarifying the interplay between quasiperiodicity and strong electron correlations. We numerically solve the Hubbard model on the Penrose-tiling structure within a real-space dynamical mean-field theory, which can deal with a spatial inhomogeneity as well as a singular self-energy necessary to describe the Mott insulator. We find that the strong correlation effect produces a charge distribution unreachable by a static mean-field approximation. In a small doping region, the spectrum shows a site-dependent gap just above the Fermi energy, which is generated by a singularly large self-energy emergent from the Mott physics and regarded as a real-space counterpart of the momentum-dependent pseudogap observed in a square-lattice Hubbard model.
We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the cellular dynamical mean-field theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum-dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ (UUU---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.
We apply the recently developed slave fermion approach to study the doped Mott insulator in the one-band Hubbard and Hubbard-Heisenberg models. Our results produce several subtle features in the electron spectra and confirm the key role of antiferromagnetic (AFM) correlations in the appearance of the pseudogap. Upon hole doping, the electron spectra exhibit a single peak near the Fermi energy in the local approximation of the Hubbard model where AFM correlations are not included. When AFM correlations are included through an explicit mean-field Heisenberg interaction, a second peak emerges at slightly lower energy and pushes the other peak to higher energy, so that a pseudogap emerges between the two peaks at small doping. Both peaks grow rapidly with increasing doping and eventually merge together, where the pseudogap no longer exists. Detailed analyses of the spectral evolution with doping and the strength of the Heisenberg interaction confirm that the lower-energy peak comes from a polaronic mechanism due to the holon-spinon interaction in the AFM-correlated background and the higher-energy peak arises from the holon hybridization to form the electron quasiparticles. Thus, the pseudogap arises from the interplay of the polaronic and hybridization mechanisms. Our results are in good agreement with previous numerical calculations using the dynamical mean-field theory and its cluster extensions, but give a clearer picture of the underlying physics. Our work provides a promising perspective for clarifying the nature of doped Mott insulators and may serve as a starting point for more elaborate investigations in the future.
Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.