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:2501.08121

Intricately Entangled Spin and Charge Diffusion and the Coherence-Incoherence Crossover in the High-Dimensional Hubbard Model

Gopal Prakash, Syed R. Hassan, M. S. Laad, N. S. Vidhyadhiraja, T. V. Ramakrishnan

Published Jan 14, 2025• 0 citations
arXivHTMLPDF

Abstract

Correlation-driven metal-insulator transitions and temperature-driven quantum-coherent-to-incoherent crossovers in correlated electron systems underpin the doping, temperature and frequency-resolved evolution of physical responses. Motivated by recent experimental studies that investigate the evolution of dynamical spin and charge responses, we analyze the spin and charge diffusion spectra in both half-filled and doped one-band Hubbard model using Dynamical Mean Field Theory (DMFT) combined with the Numerical Renormalization Group (NRG). We compare the relative strengths and limitations of Density Matrix NRG (DMNRG) and Full Density Matrix NRG (FDM-NRG) in capturing low-frequency spectral features and their evolution with temperature, interaction strength and band-filling. Key measures, including characteristic frequency scales, Kullback-Leibler divergence, diffusion constants, and kurtosis provide complementary but internally consistent picture for the evolution of spin and charge excitations across bandwidth as well as the band-filling driven Mott transitions and the coherent-incoherent crossover. We find that spin and charge fluctuations cross over from quantum-coherent-to-quantum-incoherent at distinct temperatures, providing a microscopic insight into the complex, two-stage, Fermi-to-non-Fermi liquid-to-bad metal crossovers seen in transport data, in particular in the $dc$ resistivity.

DOI
10.48550/arxiv.2501.08121

Related papers

Intricately entangled spin and charge diffusion and the coherence-incoherence crossover in the high-dimensional Hubbard model

Gopal Prakash, Syed R. Hassan, M. S. Laad +2 more

Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.

Physica Scripta•Mar 27, 2026•0 citations

Absence of a quantum limit to charge diffusion in bad metals

Nandan Pakhira, Ross H. McKenzie

Good metals are characterized by diffusive transport of coherent quasiparticle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, $\frac{ha}{{e}^{2}}$, where $a$ is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge-diffusion constant, $D\ensuremath{\gtrsim}\ensuremath{\hbar}{v}_{F}^{2}/({k}_{B}T)$, in the incoherent regime of transport, where ${v}_{F}$ is the Fermi velocity and $T$ the temperature. Using dynamical mean-field theory (DMFT) we calculate the charge-diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi-liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity ${v}_{F}$ is replaced by its low-temperature renormalized value ${v}_{F}^{*}$. The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high-temperature region where the resistivity is close to linear in temperature. Our calculated charge-diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, ${D}_{s}\ensuremath{\sim}1.3\ensuremath{\hbar}/m$, where $m$ is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.

arXiv:1409.5662•Physical Review B•Feb 23, 2015•34 citations

Finite-temperature dynamics of the Mott insulating Hubbard chain

Alberto Nocera, Fabian H. L. Eßler, Adrian E. Feiguin

We study the dynamical response of the half-filled one-dimensional Hubbard model for a range of interaction strengths $U$ and temperatures $T$ by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures $T\ensuremath{\sim}J=4{t}^{2}/U$ for sufficiently large $U>4t$. At smaller values of $U$ and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite-temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.

arXiv:1710.06452•Physical review. B./Physical review. B•Jan 29, 2018•44 citations

Finite temperature precursors of Mottness in the Fermi Hubbard model

S . M. Roy, Abhisek Samanta, Nandini Trivedi

We investigate finite-temperature precursors of Mottness in the repulsive Hubbard model above the spin-ordering temperature, using numerically exact determinant quantum Monte Carlo. We show that the finite-temperature crossover is accompanied by a pronounced suppression of charge fluctuations, despite the presence of a gapless single-particle spectra, demonstrating that Mottness first emerges via two-particle response in an anomalous metallic regime, before appearing in single-particle spectral functions. We further show that a gap formation in the density of states occurs through momentum-resolved redistribution of spectral weight across the Brillouin zone, that begins at the onset of anomalous metallic regime, rather than through gap formation in single-particle spectral functions at individual momenta. Upon doping, the anomalous-metallic regime generates transport and spectroscopic signatures characteristic of doped Mott insulators. This shows that the transport and spectroscopic anomalies of the doped Hubbard model do not require the presence of a fully formed Mott insulator at half-filling, but instead originate from the strong charge-response renormalization and spectral-weight redistribution that develop within the precursor anomalous metallic regime at half-filling.

arXiv:2606.27204•Jun 25, 2026•0 citations

Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model

Mingzhong Lu, Yu-Feng Song, Youjin Deng +1 more

The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction ($T$-$U$) plane. With increasing $U$, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing $U$. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.

arXiv:2602.22705•Physical review. B./Physical review. B•May 12, 2026•2 citations

Low quasiparticle coherence temperature in the one-band Hubbard model: A slave-boson approach

Alejandro Mezio, Ross H. McKenzie

We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight $Z$ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature ${T}_{\mathrm{coh}}$ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.

arXiv:1702.02796•Physical review. B./Physical review. B•Jul 13, 2017•12 citations
Correlation-driven metal-insulator transitions and temperature-driven quantum-coherent-to-incoherent crossovers in correlated electron systems underpin the doping, temperature and frequency-resolved evolution of physical responses. Motivated by recent experimental studies that investigate the evolution of dynamical spin and charge responses, we analyze the spin and charge diffusion spectra in both half-filled and doped one-band Hubbard model using Dynamical Mean Field Theory (DMFT) combined with the Numerical Renormalization Group (NRG). We compare the relative strengths and limitations of Density Matrix NRG (DMNRG) and Full Density Matrix NRG (FDM-NRG) in capturing low-frequency spectral features and their evolution with temperature, interaction strength and band-filling. Key measures, including characteristic frequency scales, Kullback-Leibler divergence, diffusion constants, and kurtosis provide complementary but internally consistent picture for the evolution of spin and charge excitations across bandwidth as well as the band-filling driven Mott transitions and the coherent-incoherent crossover. We find that spin and charge fluctuations cross over from quantum-coherent-to-quantum-incoherent at distinct temperatures, providing a microscopic insight into the complex, two-stage, Fermi-to-non-Fermi liquid-to-bad metal crossovers seen in transport data, in particular in the dcdcdc resistivity.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.
Good metals are characterized by diffusive transport of coherent quasiparticle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, hae2\frac{ha}{{e}^{2}}e2ha​, where aaa is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge-diffusion constant, $D\ensuremath{\gtrsim}\ensuremath{\hbar}{v}_{F}^{2}/({k}_{B}T)$, in the incoherent regime of transport, where vF{v}_{F}vF​ is the Fermi velocity and TTT the temperature. Using dynamical mean-field theory (DMFT) we calculate the charge-diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi-liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity vF{v}_{F}vF​ is replaced by its low-temperature renormalized value vF∗{v}_{F}^{*}vF∗​. The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high-temperature region where the resistivity is close to linear in temperature. Our calculated charge-diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, ${D}_{s}\ensuremath{\sim}1.3\ensuremath{\hbar}/m$, where mmm is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.
We study the dynamical response of the half-filled one-dimensional Hubbard model for a range of interaction strengths UUU and temperatures TTT by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures $T\ensuremath{\sim}J=4{t}^{2}/U$ for sufficiently large U>4tU>4tU>4t. At smaller values of UUU and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite-temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.
We investigate finite-temperature precursors of Mottness in the repulsive Hubbard model above the spin-ordering temperature, using numerically exact determinant quantum Monte Carlo. We show that the finite-temperature crossover is accompanied by a pronounced suppression of charge fluctuations, despite the presence of a gapless single-particle spectra, demonstrating that Mottness first emerges via two-particle response in an anomalous metallic regime, before appearing in single-particle spectral functions. We further show that a gap formation in the density of states occurs through momentum-resolved redistribution of spectral weight across the Brillouin zone, that begins at the onset of anomalous metallic regime, rather than through gap formation in single-particle spectral functions at individual momenta. Upon doping, the anomalous-metallic regime generates transport and spectroscopic signatures characteristic of doped Mott insulators. This shows that the transport and spectroscopic anomalies of the doped Hubbard model do not require the presence of a fully formed Mott insulator at half-filling, but instead originate from the strong charge-response renormalization and spectral-weight redistribution that develop within the precursor anomalous metallic regime at half-filling.
The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction (TTT-UUU) plane. With increasing UUU, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing UUU. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.
We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight ZZZ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature Tcoh{T}_{\mathrm{coh}}Tcoh​ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.