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:2005.05984 · Physical review. B./Physical review. B

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Michele Fava, Brayden Ware, Sarang Gopalakrishnan, Romain Vasseur, S. A. Parameswaran

Published Sep 10, 2020• 58 citations
arXivHTMLPDF

Abstract

Using the framework of generalized hydrodynamics for integrable systems, the authors study finite-temperature transport in the 1D Hubbard model. At strong coupling, the authors characterize transport in the spin-incoherent regime -- where spin degrees of freedom are ``hot'' while charge degrees of freedom are ``cold'' -- and its crossover to the Luttinger liquid regime. Furthermore, using a combination of analytical arguments and numerical simulations, the authors show that when the Hamiltonian features a spin or $\ensuremath{\eta}$-pairing SU(2) symmetry or both, spin or charge transport is superdiffusive with Kardar-Parisi-Zhang scaling.

DOI
10.1103/physrevb.102.115121

Related papers

Finite-temperature spin and charge transport in integrable one-dimensional Mott–Hubbard insulators

J. M. P. Carmelo, Pedro D Sacramento

The one-dimensional (1D) Hubbard model at zero magnetic field, h=0, and zero chemical potential, μ=0, and, thus, at the h=μ=0[SO(4)×U(1)]/Z2-symmetry point, is the paradigmatic quantum system for low-dimensional strongly correlated electron 1D Mott-Hubbard insulators. Studies relying on hydrodynamic theory and Kardar-Parisi-Zhang (KPZ) scaling have found that for the 1D Hubbard model at the h=μ=0 point, both spin and charge transports are for all temperatures T>0 that are anomalous superdiffusive. In this paper, we review recent results that correct the hydrodynamic theory and KPZ scaling prediction concerning the finite-temperature charge transport, as it is normal diffusive for all finite temperatures T>0. This failure of the hydrodynamic theory and KPZ scaling stems from the misleading assumption that the h=μ=0[SO(4)×U(1)]/Z2-symmetry point rather is a h=μ=0SO(4)-symmetry point. Such an assumption has ignored the quantum effects associated with the τ-translational U(1) symmetry beyond SO(4).

Chaos An Interdisciplinary Journal of Nonlinear Science•Nov 1, 2025•1 citation

Finite-temperature transport in gapless and gapped 1D integrable quantum systems

J. M. P. Carmelo

Abstract Generalized hydrodynamics (GHD) has successfully addressed several open questions regarding finite-temperature ( T > 0) transport in one-dimensional (1D) integrable models, including the mechanisms behind anomalous superdiffusive transport. However, disagreements persist concerning finite-temperature charge transport in the 1D Hubbard model at zero chemical potential ( µ = 0). These disagreements do not arise from the GHD framework itself but rather from differing treatments of the model’s global symmetry at the h = μ = 0 point, where h is the magnetic field. Specifically, the controversy concerns whether finite-temperature charge transport at µ = 0 is anomalous superdiffusive, as predicted using GHD when only the SU (2) × SU (2) symmetries are considered, or instead normal diffusive, as found when employing a representation that fully accounts for the model’s global [ SU (2) × SU (2) × U (1)]/ Z 2 2 symmetry at h = μ = 0 . This work aims to contribute to resolving this issue and advancing the understanding of transport in such systems. We begin by briefly reviewing GHD and other methods predictions regarding anomalous superdiffusive spin transport at finite temperature in gapless 1D integrable models such as the spin- 1 / 2 XXX chain at h = 0 and the 1D Hubbard model at h = μ = 0 . We then review T > 0 transport results in gapped 1D integrable models, focusing on charge transport in the 1D Hubbard model at h = μ = 0 and spin transport in the spin- 1 / 2 XXZ chain at h = 0 with anisotropy Δ > 1 . We identify and discuss the origin of the aforementioned discrepancies, showing how their resolution leads to a deeper understanding of anomalous superdiffusion.

Reports on Progress in Physics•Mar 1, 2026•2 citations

Diffusive charge transport in the gapped one-dimensional Hubbard model at all finite temperatures

J. M. P. Carmelo, Pedro D Sacramento

Studies relying on hydrodynamic theory and Kardar-Parisi-Zhang (KPZ) scaling have found that in the one-dimensional Hubbard model spin and charge transport are for all temperatures T > 0 anomalous superdiffusive at zero magnetic field, h = 0, and zero chemical potential, μ = 0, respectively. However, this contradicts recent exact results that at very low temperature charge transport rather is normal diffusive. In this Letter we identify the mechanisms that control the different types of temperature dependence of the h = 0 spin and μ = 0 charge transport and find that the latter is normal diffusive for all finite temperatures T > 0, in contrast to the hydrodynamic theory and KPZ scaling predictions.

arXiv:2507.02753•Physical review. B./Physical review. B•Jun 12, 2025•6 citations

Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

Sarang Gopalakrishnan, Romain Vasseur

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

arXiv:2305.15463•Annual Review of Condensed Matter Physics•Nov 21, 2023•21 citations

Finite-temperature charge and spin transport in the one-dimensional Hubbard model accounting for its global [ SU ( 2 ) × SU ( 2 ) × U ( 1 ) ]/ Z 2 2 symmetry

J. M. P. Carmelo, J. E. C. Carmelo

Most studies on the one-dimensional (1D) Hubbard model with transfer integral $t$ and on-site repulsion $U$ have assumed that for $u=U/4t>0$ and $h=\ensuremath{\mu}=0$, where $h$ denotes the magnetic field and $\ensuremath{\mu}$ the chemical potential, its global symmetry is $\mathrm{SO}(4)=[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)]/{Z}_{2}$. However, both in 1D and for the $U>0$ Hubbard model on any bipartite lattice it is actually larger and given by $[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]/{Z}_{2}^{2}=[\mathrm{SO}(4)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]/{Z}_{2}$. The studies of this paper account for the irreducible representations of that symmetry to identify both the spin and charge carriers that populate each of the energy eigenstates that span that model full Hilbert space. The global $\ensuremath{\tau}$-translational U(1) symmetry beyond $\mathrm{SO}(4)$ is found to describe the relative translational degrees of freedom of such spin and charge carriers, respectively. We show that important finite-temperature transport quantities as the $h>0$ spin and $\ensuremath{\mu}>0$ charge stiffnesses and the $h=0$ spin and $\ensuremath{\mu}=0$ charge diffusion constants are controlled by microscopic processes associated with the spin and charge elementary currents carried by these spin and charge carriers, respectively. We describe the model finite-temperature transport properties in terms of the microscopic processes associated with the spin and charge elementary currents carried by the corresponding carriers. We expect that the general $\ensuremath{\tau}$- and physical $\ensuremath{\alpha}$-spin representation used in our study is that suitable to address the open problems on finite-temperature transport in the 1D Hubbard model also discussed in this paper.

arXiv:2503.21573•Physical review. B./Physical review. B•Mar 26, 2025•7 citations

Temperature dependence of charge transport in the half-filled one-dimensional Hubbard model

J. M. P. Carmelo, Pedro D Sacramento

The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant $D$ of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature $T>0$, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}$ is the Mott-Hubbard gap. It only diverges in the $T\ensuremath{\rightarrow}0$ limit, being finite and decreasing upon increasing $T$ within the ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ regime. Our exact results both provide valuable physical information on a complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ to anomalous superdiffusive in the ${k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

arXiv:2411.10783•Physical review. B./Physical review. B•Nov 15, 2024•10 citations
Using the framework of generalized hydrodynamics for integrable systems, the authors study finite-temperature transport in the 1D Hubbard model. At strong coupling, the authors characterize transport in the spin-incoherent regime -- where spin degrees of freedom are hot'' while charge degrees of freedom are cold'' -- and its crossover to the Luttinger liquid regime. Furthermore, using a combination of analytical arguments and numerical simulations, the authors show that when the Hamiltonian features a spin or \ensuremathη\ensuremath{\eta}\ensuremathη-pairing SU(2) symmetry or both, spin or charge transport is superdiffusive with Kardar-Parisi-Zhang scaling.
The one-dimensional (1D) Hubbard model at zero magnetic field, h=0, and zero chemical potential, μ=0, and, thus, at the h=μ=0[SO(4)×U(1)]/Z2-symmetry point, is the paradigmatic quantum system for low-dimensional strongly correlated electron 1D Mott-Hubbard insulators. Studies relying on hydrodynamic theory and Kardar-Parisi-Zhang (KPZ) scaling have found that for the 1D Hubbard model at the h=μ=0 point, both spin and charge transports are for all temperatures T>0 that are anomalous superdiffusive. In this paper, we review recent results that correct the hydrodynamic theory and KPZ scaling prediction concerning the finite-temperature charge transport, as it is normal diffusive for all finite temperatures T>0. This failure of the hydrodynamic theory and KPZ scaling stems from the misleading assumption that the h=μ=0[SO(4)×U(1)]/Z2-symmetry point rather is a h=μ=0SO(4)-symmetry point. Such an assumption has ignored the quantum effects associated with the τ-translational U(1) symmetry beyond SO(4).
Abstract Generalized hydrodynamics (GHD) has successfully addressed several open questions regarding finite-temperature ( T > 0) transport in one-dimensional (1D) integrable models, including the mechanisms behind anomalous superdiffusive transport. However, disagreements persist concerning finite-temperature charge transport in the 1D Hubbard model at zero chemical potential ( µ = 0). These disagreements do not arise from the GHD framework itself but rather from differing treatments of the model’s global symmetry at the h = μ = 0 point, where h is the magnetic field. Specifically, the controversy concerns whether finite-temperature charge transport at µ = 0 is anomalous superdiffusive, as predicted using GHD when only the SU (2) × SU (2) symmetries are considered, or instead normal diffusive, as found when employing a representation that fully accounts for the model’s global [ SU (2) × SU (2) × U (1)]/ Z 2 2 symmetry at h = μ = 0 . This work aims to contribute to resolving this issue and advancing the understanding of transport in such systems. We begin by briefly reviewing GHD and other methods predictions regarding anomalous superdiffusive spin transport at finite temperature in gapless 1D integrable models such as the spin- 1 / 2 XXX chain at h = 0 and the 1D Hubbard model at h = μ = 0 . We then review T > 0 transport results in gapped 1D integrable models, focusing on charge transport in the 1D Hubbard model at h = μ = 0 and spin transport in the spin- 1 / 2 XXZ chain at h = 0 with anisotropy Δ > 1 . We identify and discuss the origin of the aforementioned discrepancies, showing how their resolution leads to a deeper understanding of anomalous superdiffusion.
Studies relying on hydrodynamic theory and Kardar-Parisi-Zhang (KPZ) scaling have found that in the one-dimensional Hubbard model spin and charge transport are for all temperatures T > 0 anomalous superdiffusive at zero magnetic field, h = 0, and zero chemical potential, μ = 0, respectively. However, this contradicts recent exact results that at very low temperature charge transport rather is normal diffusive. In this Letter we identify the mechanisms that control the different types of temperature dependence of the h = 0 spin and μ = 0 charge transport and find that the latter is normal diffusive for all finite temperatures T > 0, in contrast to the hydrodynamic theory and KPZ scaling predictions.
The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.
Most studies on the one-dimensional (1D) Hubbard model with transfer integral ttt and on-site repulsion UUU have assumed that for u=U/4t>0u=U/4t>0u=U/4t>0 and $h=\ensuremath{\mu}=0$, where hhh denotes the magnetic field and $\ensuremath{\mu}$ the chemical potential, its global symmetry is $\mathrm{SO}(4)=[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)]/{Z}_{2}$. However, both in 1D and for the U>0U>0U>0 Hubbard model on any bipartite lattice it is actually larger and given by $[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]/{Z}_{2}^{2}=[\mathrm{SO}(4)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]/{Z}_{2}$. The studies of this paper account for the irreducible representations of that symmetry to identify both the spin and charge carriers that populate each of the energy eigenstates that span that model full Hilbert space. The global $\ensuremath{\tau}$-translational U(1) symmetry beyond SO(4)\mathrm{SO}(4)SO(4) is found to describe the relative translational degrees of freedom of such spin and charge carriers, respectively. We show that important finite-temperature transport quantities as the h>0h>0h>0 spin and $\ensuremath{\mu}>0$ charge stiffnesses and the h=0h=0h=0 spin and $\ensuremath{\mu}=0$ charge diffusion constants are controlled by microscopic processes associated with the spin and charge elementary currents carried by these spin and charge carriers, respectively. We describe the model finite-temperature transport properties in terms of the microscopic processes associated with the spin and charge elementary currents carried by the corresponding carriers. We expect that the general $\ensuremath{\tau}$- and physical $\ensuremath{\alpha}$-spin representation used in our study is that suitable to address the open problems on finite-temperature transport in the 1D Hubbard model also discussed in this paper.
The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant DDD of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature T>0T>0T>0, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}$ is the Mott-Hubbard gap. It only diverges in the $T\ensuremath{\rightarrow}0$ limit, being finite and decreasing upon increasing TTT within the ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ regime. Our exact results both provide valuable physical information on a complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ to anomalous superdiffusive in the ${k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.