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arXiv:1206.4372

Thermalization Breakdown and Conductivity Improvement within the Interacting Dynamic Disorder Model

Yao Yao, Yiqiang Zhan, X. Y. Hou, Chang-Qin Wu

Published Jun 20, 2012• 0 citations
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Abstract

Based on the framework of Kubo formulism, we develop the minimally entangled typical thermal state algorithm to study the temperature and time dependence of current-current correlation function in one-dimensional spinless fermion model, taking into account both the electron-electron (e-e) intersite interaction and the dynamic disorder induced by classical phonons. Without e-e interaction, the numerical results, showing an exponential decay of the time dependent correlation, could be precisely compared with that from the analytical derivation, namely, from the generalized Langevin equation. More importantly, when a strong enough e-e interaction is presence, we find a long-time correlation in the regime of small dynamic disorder, indicating the breakdown of thermal relaxation, which is a typical many-body effect. On the basis of this finding, we show that it might be applied to understand the metalliclike charge transport and the abnormal improvement of the conductivity with respect to the redoping experiment in K$_3$C$_{60}$, an organic superconducting material.

DOI
10.48550/arxiv.1206.4372

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Based on the framework of Kubo formulism, we develop the minimally entangled typical thermal state algorithm to study the temperature and time dependence of current-current correlation function in one-dimensional spinless fermion model, taking into account both the electron-electron (e-e) intersite interaction and the dynamic disorder induced by classical phonons. Without e-e interaction, the numerical results, showing an exponential decay of the time dependent correlation, could be precisely compared with that from the analytical derivation, namely, from the generalized Langevin equation. More importantly, when a strong enough e-e interaction is presence, we find a long-time correlation in the regime of small dynamic disorder, indicating the breakdown of thermal relaxation, which is a typical many-body effect. On the basis of this finding, we show that it might be applied to understand the metalliclike charge transport and the abnormal improvement of the conductivity with respect to the redoping experiment in K3_33​C60_{60}60​, an organic superconducting material.
Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing dc transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the dc conductivity ${\ensuremath{\sigma}}_{0}$ scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase in the effective localization length with the interaction.
We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.
The minimally entangled typical thermal states algorithm is applied to fermionic systems using the Krylov-space approach to evolve the system in imaginary time. The convergence of local observables is studied in a tight-binding system with a site-dependent potential. The temperature dependence of the superconducting correlations of the attractive Hubbard model is analyzed on chains, showing an exponential decay with distance and exponents proportional to the temperature at low temperatures, as expected. In addition, the nonlocal parity correlator is calculated at finite temperature. Other possible applications of the minimally entangled typical thermal states algorithm to fermionic systems are also discussed.
We study the real-time dynamics of local occupation numbers in a one-dimensional model of spinless fermions with a random on-site potential for a certain class of initial states. The latter are thermal (mixed or pure) states of the model in the presence of an additional static force but become nonequilibrium states after a sudden removal of this static force. For this class and high temperatures, we show that the induced dynamics is given by a single correlation function at equilibrium, independent of the initial expectation values being prepared close to equilibrium (by a weak static force) or far away from equilibrium (by a strong static force). Remarkably, this type of universality holds true in both the ergodic phase and the many-body localized regime. Moreover, it does not depend on the specific choice of a unit cell for the local density. We particularly discuss two important consequences. First, the long-time expectation value of the local density is uniquely determined by the fluctuations of its diagonal matrix elements in the energy eigenbasis. Thus, the validity of the eigenstate thermalization hypothesis is not only a sufficient but also a necessary condition for thermalization. Second, the real-time broadening of density profiles is always given by the current autocorrelation function at equilibrium via a generalized Einstein relation. In the context of transport, we discuss the influence of disorder for large particle-particle interactions, where normal diffusion is known to occur in the disorder-free case. Our results suggest that normal diffusion is stable against weak disorder, while they are consistent with anomalous diffusion for stronger disorder below the localization transition. Particularly, for weak disorder, Gaussian density profiles can be observed for single disorder realizations, which we demonstrate for finite lattices up to 31 sites.
We consider heat transfer in one-dimensional systems with long-range interactions. It is known that typical short-range interacting systems shows anomalous behavior in heat transport when total momentum is conserved, whereas momentum-nonconserving systems do not exhibit anomaly. In this study, we focus on the effect of long-range interaction. We propose an exactly solvable model that reduces to the so-called momentum-exchange model in the short-range interaction limit. We exactly calculate the asymptotic time decay in the energy current correlation function, which is related to the thermal conductivity via the Green-Kubo formula. From the time decay of the current correlation, we show three qualitatively crucial results. First, the anomalous exponent in the time-decay continuously changes as a function of the index of the long-range interaction. Second, there is a regime where the current correlation diverges with increasing the system size with fixed time, and hence, the exponent of the time decay cannot be defined. Third, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport. Higher dimensions are also considered, and we found that long-range interaction can induce the anomalous exponent even in three-dimensional systems.
Heavy doping in organic materials induces complex many-body interactions characterized by the coexistence of strong electron correlation and electron-phonon coupling, arising from their soft structures and low dielectric constants. Simulating charge transport and thermopower in this regime poses a significant computational challenge. In this work, we propose a finite-temperature time-dependent tree tensor network state (TTNS) method to calculate the conductivity and Seebeck coefficient of organic materials modeled by the Holstein-Hubbard Hamiltonian. Our TTNS ansatz features a tailored “bus-branch” structure, where the “bus” captures the electronic entanglement, and the “branches” encode the local electron-phonon correlations. Benchmarks against exact diagonalization (ED) on small clusters demonstrate that this network structure achieves numerically exact results with smaller bond dimensions than the Matrix Product States (MPS). Furthermore, the “branch” topology efficiently isolates the local electron-phonon entanglement, thereby avoiding the globally large bond dimensions required by MPS. These algorithmic advantages enable us to constrain the relative error of transport properties to within 10% across a wide range of parameter regimes. To validate the capability of this framework, we study the complex interplay between Hubbard repulsion and phonon-mediated attraction, successfully illustrating the roles of spin degrees of freedom and effective interactions in thermodynamics and charge transport, and reproducing the correlation-induced anomalous sign change of the Seebeck coefficient. Our work establishes the “bus-branch” TTNS as a powerful and efficient tool for exploring quantum dynamics in strongly correlated electron-phonon systems.