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arXiv:1401.0121

The ground state structure of electron's ensemble on one-dimension disordered lattice

Leonid Andreevich Pastur, Victor V. Slavin, A. A. Krivchikov

Published Dec 31, 2013• 0 citations
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Abstract

The ground state of interacting particles on a disordered one-dimensional host-lattice is studied by a direct numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal, replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

DOI
10.48550/arxiv.1401.0121

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The ground state of interacting particles on a disordered one-dimensional host-lattice is studied by a direct numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal, replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.
The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.
New numerical methods of the ground state and thermodynamic properties calculations of one-dimensional Generalized Wigner crystal on disordered host-lattice are proposed. Unlike computer simulation methods (for instance, Monte Carlo) these methods bring the exact results. Another attractive feature of the proposed methods is their speed: it is possible to study the systems with length about 104–105 nodes even on a personal computer. This is especially important in the case of weakly disordered systems and the long-range correlations. The gapless structure of low-energy excitation and breaking long-range correlations at arbitrary small disordering are established.
The influence of disorder in host-lattice sites on the ground state properties of onedimensional electron lattice gas has been studied. Numeric calculations of partition functions for the systems with ~104 particles have been carried out. It is shown that arbitrary weak disorder in host-lattice site positions leads to formation of electron blocks (“domains”) which destroy long-range order. Mean “domains” length is about 1/a4, where a is typical disorder in host-lattice sites positions. The calculations have been carried out using new effective method for the ground state structure and lowtemperature thermodynamic properties investigations. The method is based on the introduction of weak external non-homogeneous filed into Hamiltonian of the system. Keywords: electron gas, disordered systems, low-dimensional systems, generalized Wigner crystal, extended Hubbard model.
The low-temperature thermodynamics of a one-dimensional electron gas on a disordered lattice, which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the partition function as a product of random transfer-matrixes, has been developed for calculations of thermodynamic characteristics of the system under consideration. The lattice structures were varied from completely chaotic up to the strictly regular one. It has been established that for any degree of disorder the entropy and heat capacity of the system tend to zero linearly as the temperature is reduced. The conclusion about the gapless character of the elementary excitations spectrum has been made. An instability of one-dimensional electron gas on a disordered lattice has been revealed: under conditions of vanishingly small disordering of the lattice, the long-range order in the systems under consideration is broken by frustrations that are one-dimensional analogues of the frustrations in two- and three-dimensional spin glasses.
We numerically investigate a one-dimensional Anderson–Hubbard model under harmonic confinement. The effects of disorder on the ground-state properties are studied for Gaussian-correlated disorder and random impurities upon changing the amplitude of the disorder strength, the correlation length or the number of impurities. For a large disorder correlation length, both the band- and Mott-insulating phases re-enter naturally as a result of a smooth long-range correlated disorder. For the randomly distributed impurities in a system of composite Mott- and band-insulating phases, we find that the band-insulating region is rapidly destroyed while the Mott region is more robust against the increase of impurities. The fluid regions are less affected in this case.
We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the low- and high-density regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov--de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For high densities, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective high-density field equations for the excitations and generalize to higher dimensions.