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

Physical review. B, Condensed matter

Conductivity and Hall effect in the two-dimensional Hubbard model

Puru Voruganti, A. A. Golubentsev, Sajeev John

Published Jun 15, 1992• 58 citations
Publisher

Abstract

A path-integral field-theoretic derivation of electromagnetic linear response for the two-dimensional Hubbard model is given. We find, remarkably, that changes in the Fermi-surface topology associated with incommensurate planar spin-density-wave saddle points induce a change in sign of the Hall coefficient at dopings ${\mathrm{\ensuremath{\delta}}}_{\mathit{H}}$=0.02--0.5 for U/t=2--10. The change in sign is not affected by short-range magnetic domains. We delinate from first principles an anomalous temperature dependence of the Hall carrier density at dopings close to ${\mathrm{\ensuremath{\delta}}}_{\mathit{H}}$. An additional anisotropic component to the usual dc conductivity is nonvanishing for certain types of spirals. The paper extends the Bloch-Boltzmann theory to the case of untraditional Fermi liquids where the damping of the quasiparticles is \ensuremath{\Gamma}(\ensuremath{\epsilon})\ensuremath{\sim}max(${\mathit{k}}_{\mathit{B}}$T,\ensuremath{\epsilon}).

DOI
10.1103/physrevb.45.13945

Related papers

DC Hall coefficient of the strongly correlated Hubbard model

Wen O. Wang, Jixun K. Ding, Brian Moritz +2 more

Abstract The Hall coefficient is related to the effective carrier density and Fermi surface topology in non-interacting and weakly interacting systems. In strongly correlated systems, the relation between the Hall coefficient and single-particle properties is less clear. Clarifying this relation would give insight into the nature of transport in strongly correlated materials that lack well-formed quasiparticles. In this work, we investigate the DC Hall coefficient of the Hubbard model using determinant quantum Monte Carlo in conjunction with a recently developed expansion of magneto-transport coefficients in terms of thermodynamic susceptibilities. At leading order in the expansion, we observe a change of sign in the Hall coefficient as a function of temperature and interaction strength, which we relate to a change in the topology of the apparent Fermi surface. We also combine our Hall coefficient results with optical conductivity values to evaluate the Hall angle, as well as effective mobility and effective mass based on Drude theory of metals.

arXiv:2002.12289•npj Quantum Materials•Jul 24, 2020•24 citations

Hall coefficient and resistivity in the doped bilayer Hubbard model

Yin Shi, Jonathan Schirmer, Long‐Qing Chen

Abstract Finding and understanding non-Fermi liquid transport behaviors are at the core of condensed matter physics. Most of the existing studies were devoted to the monolayer Hubbard model, which is the simplest model that captures essential features of high-temperature superconductivity. Here we discover a new type of non-Fermi liquid behavior emergent in the hole-doped bilayer Hubbard model, using dynamical mean-field theory with a full consideration of the short-range interlayer electron correlation. We find that at low temperatures, the Hall coefficient has a strong nonmonotonic dependence on temperature, leading to a double or quadruple reversal of its sign depending on the doping level. At the same time, the resistivity exhibits two plateaus rather than linearity in its temperature dependence. We show that these intriguing transport behaviors stem from the formation of coherent interlayer singlets, which scatter off gapped collective modes arising from short-range interlayer antiferromagnetic fluctuations.

arXiv:2308.03862•Physical review. B./Physical review. B•Feb 7, 2024•2 citations

Optical and Hall conductivity of the two dimensional Hubbard model: effective theory description, sign-problem-free Monte Carlo simulation and applications to the cuprate superconductors

Xinyue Liu, Tao Li

Exact formulas for the optical conductivity and the Hall conductivity of the two dimensional Hubbard model are derived in terms of an effective theory description of the local moment fluctuation in the system. In this framework, the quantum Monte Carlo simulation of the electromagnetic response of such a strongly correlated electron system becomes sign-problem-free in many physically relevant cases. In particular, it is sign-problem-free when we assume the widely used Millis-Monien-Pines form for the phenomenological susceptibility in the effective action of the fluctuating local moment, even though these local moments are now subjected to Landau damping as a result of their coupling to the itinerant quasiparticle on the fermi surface. This is true more generally when a $φ^{4}$ term is included in the effective action and is thus not restricted to the Gaussian limit. Here we demonstrate the power of this framework by studying the effect of thermal fluctuation of the local moment on the optical conductivity $σ^{xx}(ω)$ and the Hall conductivity $σ^{xy}(ω)$ of the cuprate superconductors. Both $σ^{xx}(ω)$ and $σ^{xy}(ω)$ calculated are found to exhibit a two-component structure, with a Drude component at low energy and a mid-infrared component at higher energy. Depending on the relative importance of the hole pocket and the electron pocket on the reconstructed fermi surface and the coupling strength to the local moment, the Drude component in $\mathrm{Im}σ^{xy}(ω)$ can be either positive or negative.(full-length abstract can be found in the main text.)

arXiv:2602.17959•Feb 20, 2026•0 citations

Spiral antiferromagnetism and the doping-induced closure of the Mott-Hubbard gap

Sajeev John, Puru Voruganti

In a 1/S loop expansion of the two-dimensional Hubbard model, doping leads to incommensurate twist spin-density-wave (SDW) states at the saddle point. Further doping reduces the on-site magnetization and increases the SDW pitch, conspiring to close the effective Mott-Hubbard gap at \ensuremath{\delta}\ensuremath{\sim}0.07--0.30 for U/t\ensuremath{\sim}2.5--10. At the one-loop level, the two massless fluctuations map to the nonlinear \ensuremath{\sigma} model at zero doping while for the twist SDW states, three massless spin-wave modes arise which are strongly coupled to the charge fluctuations, therefore implying nontrivial charge-spin response functions for the metal.

Physical review. B, Condensed matter•May 1, 1991•14 citations

Spectral properties of the two-dimensional Hubbard model

V. Zlatić, K. D. Schotte, Gudrun Schliecker

The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.

Physical review. B, Condensed matter•Aug 1, 1995•25 citations

Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties

B. Sriram Shastry, Peizhi Mai

Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.

arXiv:1703.08142•New Journal of Physics•Nov 17, 2017•11 citations
A path-integral field-theoretic derivation of electromagnetic linear response for the two-dimensional Hubbard model is given. We find, remarkably, that changes in the Fermi-surface topology associated with incommensurate planar spin-density-wave saddle points induce a change in sign of the Hall coefficient at dopings \ensuremathδH{\mathrm{\ensuremath{\delta}}}_{\mathit{H}}\ensuremathδH​=0.02--0.5 for U/t=2--10. The change in sign is not affected by short-range magnetic domains. We delinate from first principles an anomalous temperature dependence of the Hall carrier density at dopings close to \ensuremathδH{\mathrm{\ensuremath{\delta}}}_{\mathit{H}}\ensuremathδH​. An additional anisotropic component to the usual dc conductivity is nonvanishing for certain types of spirals. The paper extends the Bloch-Boltzmann theory to the case of untraditional Fermi liquids where the damping of the quasiparticles is \ensuremath{\Gamma}(\ensuremath{\epsilon})\ensuremath{\sim}max(kB{\mathit{k}}_{\mathit{B}}kB​T,\ensuremath{\epsilon}).
Abstract The Hall coefficient is related to the effective carrier density and Fermi surface topology in non-interacting and weakly interacting systems. In strongly correlated systems, the relation between the Hall coefficient and single-particle properties is less clear. Clarifying this relation would give insight into the nature of transport in strongly correlated materials that lack well-formed quasiparticles. In this work, we investigate the DC Hall coefficient of the Hubbard model using determinant quantum Monte Carlo in conjunction with a recently developed expansion of magneto-transport coefficients in terms of thermodynamic susceptibilities. At leading order in the expansion, we observe a change of sign in the Hall coefficient as a function of temperature and interaction strength, which we relate to a change in the topology of the apparent Fermi surface. We also combine our Hall coefficient results with optical conductivity values to evaluate the Hall angle, as well as effective mobility and effective mass based on Drude theory of metals.
Abstract Finding and understanding non-Fermi liquid transport behaviors are at the core of condensed matter physics. Most of the existing studies were devoted to the monolayer Hubbard model, which is the simplest model that captures essential features of high-temperature superconductivity. Here we discover a new type of non-Fermi liquid behavior emergent in the hole-doped bilayer Hubbard model, using dynamical mean-field theory with a full consideration of the short-range interlayer electron correlation. We find that at low temperatures, the Hall coefficient has a strong nonmonotonic dependence on temperature, leading to a double or quadruple reversal of its sign depending on the doping level. At the same time, the resistivity exhibits two plateaus rather than linearity in its temperature dependence. We show that these intriguing transport behaviors stem from the formation of coherent interlayer singlets, which scatter off gapped collective modes arising from short-range interlayer antiferromagnetic fluctuations.
Exact formulas for the optical conductivity and the Hall conductivity of the two dimensional Hubbard model are derived in terms of an effective theory description of the local moment fluctuation in the system. In this framework, the quantum Monte Carlo simulation of the electromagnetic response of such a strongly correlated electron system becomes sign-problem-free in many physically relevant cases. In particular, it is sign-problem-free when we assume the widely used Millis-Monien-Pines form for the phenomenological susceptibility in the effective action of the fluctuating local moment, even though these local moments are now subjected to Landau damping as a result of their coupling to the itinerant quasiparticle on the fermi surface. This is true more generally when a φ4φ^{4}φ4 term is included in the effective action and is thus not restricted to the Gaussian limit. Here we demonstrate the power of this framework by studying the effect of thermal fluctuation of the local moment on the optical conductivity σxx(ω)σ^{xx}(ω)σxx(ω) and the Hall conductivity σxy(ω)σ^{xy}(ω)σxy(ω) of the cuprate superconductors. Both σxx(ω)σ^{xx}(ω)σxx(ω) and σxy(ω)σ^{xy}(ω)σxy(ω) calculated are found to exhibit a two-component structure, with a Drude component at low energy and a mid-infrared component at higher energy. Depending on the relative importance of the hole pocket and the electron pocket on the reconstructed fermi surface and the coupling strength to the local moment, the Drude component in Imσxy(ω)\mathrm{Im}σ^{xy}(ω)Imσxy(ω) can be either positive or negative.(full-length abstract can be found in the main text.)
In a 1/S loop expansion of the two-dimensional Hubbard model, doping leads to incommensurate twist spin-density-wave (SDW) states at the saddle point. Further doping reduces the on-site magnetization and increases the SDW pitch, conspiring to close the effective Mott-Hubbard gap at \ensuremath{\delta}\ensuremath{\sim}0.07--0.30 for U/t\ensuremath{\sim}2.5--10. At the one-loop level, the two massless fluctuations map to the nonlinear \ensuremath{\sigma} model at zero doping while for the twist SDW states, three massless spin-wave modes arise which are strongly coupled to the charge fluctuations, therefore implying nontrivial charge-spin response functions for the metal.
The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) is momentum dependent. Using Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.
Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.