Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large $U$ limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping ${p}_{c}$ depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large- $N$ model with distinct non-Fermi-liquid properties. We show that this model has linear-in- $T$ resistivity with doping-dependent slope maximized at $p={p}_{c}$ and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large $U$ limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping ${p}_{c}$ depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-$N$ model with distinct non-Fermi-liquid properties. We show that this model has linear-in-$T$ resistivity with doping-dependent slope maximized at $p={p}_{c}$ and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.

arXiv:2402.18626Physical review. B./Physical review. BOct 15, 20240 citations

Doping dependence of on-site quantities in the two-dimensional Hubbard model

Francesco Paolo Mancini, S. Marra, H. Matsumoto

Physica C SuperconductivityMar 1, 199544 citations

Entropy in the Non-Fermi-Liquid Regime of the Doped 2D Hubbard Model

Connor Lenihan, Aaram J. Kim, Fedor Šimkovic +1 more

We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.

arXiv:2001.09948Physical Review LettersMar 12, 202117 citations

Quantum Criticality in Strongly Correlated Electron Systems

Samuel Kellar

The study of the Hubbard model in three dimensions contains a variety of phases dependent upon the chosen parameters. This thesis shows that there is the indication of a zero temperature phase transition at a finite doping. The Hubbard model has been used to identify a similar quantum critical point in two dimensions. The presented results continue these investigations. The system demonstrates a strange metal phase at finite temperature which cannot be described in term of the conventional Fermi liquid. While there have been extensive studies over the past three decades for such materials in two dimensions, there are few numerical studies in three dimensions. This study strives to identify the existence of the strange metal beyond two dimensions. In this work we present numerical results based on the dynamical cluster approximation to demonstrate the existence of a strange metal phase in three dimensions.The study of the Hubbard model in three dimensions contains a variety of phases dependent upon the chosen parameters. This thesis shows that there is the indication of a zero temperature phase transition at a finite doping. The Hubbard model has been used to identify a similar quantum critical point in two dimensions. The presented results continue these investigations. The system demonstrates a strange metal phase at finite temperature which cannot be described in term of the conventional Fermi liquid. While there have been extensive studies over the past three decades for such materials in two dimensions, there are few numerical studies in three dimensions. This study strives to identify the existence of the strange metal beyond two dimensions. In this work we present numerical results based on the dynamical cluster approximation to demonstrate the existence of a strange metal phase in three dimensions.

Civil War Book ReviewJul 6, 20200 citations

U

limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping

{p}_{c}

depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-

N

model with distinct non-Fermi-liquid properties. We show that this model has linear-in-

T

resistivity with doping-dependent slope maximized at

p={p}_{c}

and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.