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

New Journal of Physics

Correlated charge transfer along molecular chains

Lothar Mühlbacher, Joachim Ankerhold

Published Jun 30, 2008• 2 citations
Publisher

Abstract

The nonequilibrium dynamics of charges along one-dimensional tight-binding lattices subject to a vibronic background is analyzed in the two-particle sector of a dissipative Hubbard model. The role of symmetries for distinguishable fermions with opposite spins and for indistinguishable ones with polarized spins is revealed and is shown to cause transfer dynamics with non-Boltzmann types of asymptotic distributions. Explicit results are obtained within an improved path integral Monte Carlo approach and are compared against an approximate description in terms of rate equations.

DOI
10.1088/1367-2630/10/6/065023

Related papers

Nonequilibrium many-body dynamics along a dissipative Hubbard chain: Symmetries and quantum Monte Carlo simulations

Lothar Mühlbacher, Joachim Ankerhold

The nonequilibrium dynamics of correlated charge transfer along a one-dimensional chain in the presence of a phonon environment is investigated within a dissipative Hubbard model. For this generalization of the ubiquitous spin-boson model the crucial role of symmetries is analyzed in detail and corresponding invariant subspaces are identified. It is shown that the time evolution typically occurs in each of the disjunct subspaces independently leading, e.g., asymptotically to a non-Boltzmann equilibrium state. Based on these findings explicit results are obtained for two interacting electrons by means of a substantially improved real-time quantum Monte Carlo approach. In the incoherent regime an appropriate mapping of the many-body dynamics onto an isomorphic single particle motion allows for an approximate description of the numerical data in terms of rate equations. These results may lead to control schemes of charge transport in tailored quantum systems as, e.g., molecular chains or quantum dot arrays.

arXiv:cond-mat/0605166•Physical Review B•Oct 12, 2006•3 citations

Nonequilibrium Dynamics of Correlated Electron Transfer in Molecular Chains

Lothar Mühlbacher, Joachim Ankerhold, A. Komnik

The relaxation dynamics of correlated electron transport along molecular chains is studied based on a substantially improved numerically exact path integral Monte Carlo approach. As an archetypical model, we consider a Hubbard chain containing two interacting electrons coupled to a bosonic bath. For this generalization of the ubiquitous spin-boson model, non-Boltzmann equilibrium distributions are found for many-body states. By mapping the multiparticle dynamics onto an isomorphic single particle motion, this phenomenon is shown to be sensitive to particle statistics and, due to its robustness, allows for new control schemes in designed quantum aggregates.

arXiv:cond-mat/0508098•Physical Review Letters•Nov 23, 2005•25 citations

Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium

Giuliano Benenti, Giulio Casati, Tomaž Prosen +2 more

We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the $t\text{\ensuremath{-}}V$ spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism.

arXiv:0901.2032•Physical Review B•Jul 8, 2009•120 citations

Dynamical properties of two coupled Hubbard chains at half-filling

H. Endres, R. M. Noack, Werner R. Hanke +2 more

Using grand canonical quantum Monte Carlo (QMC) simulations combined with maximum entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, A(k,\ensuremath{\omega}), undergoes a qualitative change with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. For smaller ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, A(k,\ensuremath{\omega}) is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange J which is reasonably well described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral t, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and to the results of spin-wave theory for small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9508074•Physical review. B, Condensed matter•Mar 1, 1996•34 citations

Time and spatially resolved quench of the fermionic Hubbard model showing restricted equilibration

Florian Goth, Fakher F. Assaad

We investigate the quench of half-filled one-dimensional and two-dimensional fermionic Hubbard models to models without Coulomb interaction. Since the time propagation is Gaussian, we can use a variety of time-dependent quantum Monte Carlo methods to tackle this problem without generating a dynamical sign problem. Using a continuous time quantum Monte Carlo method, we achieve a system size of 128 sites in one dimension, and using a Blankenbecler-Scalapino-Sugar type algorithm, we were able to simulate $20\ifmmode\times\else\texttimes\fi{}20$ square lattices. Applying these methods to study the dynamics after the quench, we observe that the final state of the system can be reasonably well described by a thermal single-particle density matrix that takes the initial single-particle conservation laws into account. The characteristic decay toward this limit is found to be oscillatory with an additional power law decay that depends on the dimensionality. This numerically exact result is shown to compare favorably to mean-field approximations as well as to perturbation theory. Furthermore, we observe the information propagation in the one-dimensional case in the charge-charge and spin-spin correlations and find that it is linear with a velocity of roughly $v\ensuremath{\approx}4$ in units of the hopping amplitude.

arXiv:1108.2703•Physical Review B•Feb 27, 2012•29 citations

2pF and 4pF instabilities in the one-dimensional Hubbard model

J. E. Hirsch, Douglas J. Scalapino

We continue our study of correlation functions in the one-dimensional Hubbard model with the use of a Monte Carlo technique. This paper focuses on the behavior of two different particle-hole susceptibilities: the on-site charge-density response function and the nearest-neighbor charge-transfer response function. Although their behavior is predicted to be similar within weak-coupling renormalization-group theory, we find different behavior with our nonperturbative technique. In particular, the charge-transfer susceptibility shows structure at $2{p}_{F}$ for large Coulomb interactions due to spin-Peierls fluctuations, which is absent in the on-site charge-density response. We also study the effect of varying band filling, by comparing results for the $\frac{1}{4}$- filled band ($\ensuremath{\rho}=0.5$) case and the cases $\ensuremath{\rho}=0.61$ and $\ensuremath{\rho}=1$. We find, for example, that it is possible to have structure in the response function at wave vectors that are not simply related to the Fermi wave vector. We discuss the implications of our results to the interpretation of experimental results in various quasi-one-dimensional charge-transfer compounds.

Physical review. B, Condensed matter•May 15, 1984•102 citations
The nonequilibrium dynamics of charges along one-dimensional tight-binding lattices subject to a vibronic background is analyzed in the two-particle sector of a dissipative Hubbard model. The role of symmetries for distinguishable fermions with opposite spins and for indistinguishable ones with polarized spins is revealed and is shown to cause transfer dynamics with non-Boltzmann types of asymptotic distributions. Explicit results are obtained within an improved path integral Monte Carlo approach and are compared against an approximate description in terms of rate equations.
The nonequilibrium dynamics of correlated charge transfer along a one-dimensional chain in the presence of a phonon environment is investigated within a dissipative Hubbard model. For this generalization of the ubiquitous spin-boson model the crucial role of symmetries is analyzed in detail and corresponding invariant subspaces are identified. It is shown that the time evolution typically occurs in each of the disjunct subspaces independently leading, e.g., asymptotically to a non-Boltzmann equilibrium state. Based on these findings explicit results are obtained for two interacting electrons by means of a substantially improved real-time quantum Monte Carlo approach. In the incoherent regime an appropriate mapping of the many-body dynamics onto an isomorphic single particle motion allows for an approximate description of the numerical data in terms of rate equations. These results may lead to control schemes of charge transport in tailored quantum systems as, e.g., molecular chains or quantum dot arrays.
The relaxation dynamics of correlated electron transport along molecular chains is studied based on a substantially improved numerically exact path integral Monte Carlo approach. As an archetypical model, we consider a Hubbard chain containing two interacting electrons coupled to a bosonic bath. For this generalization of the ubiquitous spin-boson model, non-Boltzmann equilibrium distributions are found for many-body states. By mapping the multiparticle dynamics onto an isomorphic single particle motion, this phenomenon is shown to be sensitive to particle statistics and, due to its robustness, allows for new control schemes in designed quantum aggregates.
We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the $t\text{\ensuremath{-}}V$ spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism.
Using grand canonical quantum Monte Carlo (QMC) simulations combined with maximum entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, A(k,\ensuremath{\omega}), undergoes a qualitative change with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. For smaller ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, A(k,\ensuremath{\omega}) is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange J which is reasonably well described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral t, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and to the results of spin-wave theory for small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. \textcopyright{} 1996 The American Physical Society.
We investigate the quench of half-filled one-dimensional and two-dimensional fermionic Hubbard models to models without Coulomb interaction. Since the time propagation is Gaussian, we can use a variety of time-dependent quantum Monte Carlo methods to tackle this problem without generating a dynamical sign problem. Using a continuous time quantum Monte Carlo method, we achieve a system size of 128 sites in one dimension, and using a Blankenbecler-Scalapino-Sugar type algorithm, we were able to simulate $20\ifmmode\times\else\texttimes\fi{}20$ square lattices. Applying these methods to study the dynamics after the quench, we observe that the final state of the system can be reasonably well described by a thermal single-particle density matrix that takes the initial single-particle conservation laws into account. The characteristic decay toward this limit is found to be oscillatory with an additional power law decay that depends on the dimensionality. This numerically exact result is shown to compare favorably to mean-field approximations as well as to perturbation theory. Furthermore, we observe the information propagation in the one-dimensional case in the charge-charge and spin-spin correlations and find that it is linear with a velocity of roughly $v\ensuremath{\approx}4$ in units of the hopping amplitude.
We continue our study of correlation functions in the one-dimensional Hubbard model with the use of a Monte Carlo technique. This paper focuses on the behavior of two different particle-hole susceptibilities: the on-site charge-density response function and the nearest-neighbor charge-transfer response function. Although their behavior is predicted to be similar within weak-coupling renormalization-group theory, we find different behavior with our nonperturbative technique. In particular, the charge-transfer susceptibility shows structure at 2pF2{p}_{F}2pF​ for large Coulomb interactions due to spin-Peierls fluctuations, which is absent in the on-site charge-density response. We also study the effect of varying band filling, by comparing results for the 14\frac{1}{4}41​- filled band ($\ensuremath{\rho}=0.5$) case and the cases $\ensuremath{\rho}=0.61$ and $\ensuremath{\rho}=1$. We find, for example, that it is possible to have structure in the response function at wave vectors that are not simply related to the Fermi wave vector. We discuss the implications of our results to the interpretation of experimental results in various quasi-one-dimensional charge-transfer compounds.