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:1703.03002 · Physical review. E

Charge and spin current statistics of the open Hubbard model with weak coupling to the environment

Berislav Buča, Tomaž Prosen

Published May 25, 2017• 9 citations
arXivHTMLPDF

Abstract

Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.

DOI
10.1103/physreve.95.052141

Related papers

Transport properties of the one-dimensional Hubbard model at finite temperature

Christoph Karrasch, Dante Marvin Kennes, Joel E. Moore

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ for the integrable XXZ spin chain in its gapped phase.

arXiv:1408.1891•Physical Review B•Oct 3, 2014•56 citations

Two-dimensional Hubbard model at finite temperature: Weak, strong, and long correlation regimes

Fedor Šimkovic, Riccardo Rossi, Michel Ferrero

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature, and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at temperatures as low as $T=0.067$ and interactions up to $U=7$, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.

arXiv:2110.05863•Physical Review Research•Dec 20, 2022•45 citations

Exactly Solvable Counting Statistics in Open Weakly Coupled Interacting Spin Systems

Berislav Buča, Tomaž Prosen

We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg (XXZ) spin-1/2 chain, we explicitly derive the third-order nonlinear corrections to the current statistics.

arXiv:1309.6520•Physical Review Letters•Feb 10, 2014•51 citations

Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model

Bo Xiao, Yuan-Yao He, Antoine Georges +1 more

State-of-the-art numerical techniques suggest that charge order in the 2D Hubbard model sets in at a nonzero temperature, answering a major open question in the physics of this paradigmatic model of quantum materials.

arXiv:2202.11741•Physical Review X•Jan 24, 2023•43 citations

Integrable non-equilibrium steady state density operators for boundary driven XXZ spin chains: observables and full counting statistics

Tomaž Prosen, Berislav Buča

We will review some known exact solutions for the steady state of the open quantum Heisenberg $XXZ$ spin chain coupled to a pair of baths [Phys. Rev. Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master equation. We also review how to calculate some relevant physical observables and provide the statistics of spin current assuming the spin chain is weakly coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].

arXiv:1501.06156•Jan 25, 2015•0 citations

Strong-Coupling Expansion for the Hubbard Model

Stéphane Pairault, David Sénéchal, A.–M. S. Tremblay

A strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in $d$ dimensions and compared with numerical results in $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. Third order expansion of the Green's function suffices to exhibit both the Mott metal-insulator transition and a low-temperature regime where antiferromagnetic correlations are strong. It is predicted that some of the weak photoemission signals observed in one-dimensional systems such as ${\mathrm{SrCuO}}_{2}$ should become stronger as temperature increases away from the spin-charge separated state.

arXiv:cond-mat/9710256•Physical Review Letters•Jun 15, 1998•88 citations
Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.
We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ for the integrable XXZ spin chain in its gapped phase.
We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature, and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at temperatures as low as T=0.067T=0.067T=0.067 and interactions up to U=7U=7U=7, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.
We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg (XXZ) spin-1/2 chain, we explicitly derive the third-order nonlinear corrections to the current statistics.
We will review some known exact solutions for the steady state of the open quantum Heisenberg XXZXXZXXZ spin chain coupled to a pair of baths [Phys. Rev. Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master equation. We also review how to calculate some relevant physical observables and provide the statistics of spin current assuming the spin chain is weakly coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].
A strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in ddd dimensions and compared with numerical results in d=1d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1d=1. Third order expansion of the Green's function suffices to exhibit both the Mott metal-insulator transition and a low-temperature regime where antiferromagnetic correlations are strong. It is predicted that some of the weak photoemission signals observed in one-dimensional systems such as SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​ should become stronger as temperature increases away from the spin-charge separated state.