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International Journal of Modern Physics B

THERMODYNAMICS OF LOW-DENSITY ELECTRON GAS ON HIGHLY DISORDERED ONE-DIMENSIONAL HOST LATTICE

Victor V. Slavin, A. A. Slutskin

Published Aug 30, 2004• 1 citation

Abstract

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.

DOI: 10.1142/s0217979204026287

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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.

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.

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices---sawtooth chain and two kagom\'e chains---with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of exact many-electron ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential ${\ensuremath{\mu}}_{0}$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact-diagonalization data for finite systems.

The thermodynamic properties of the two-dimensional Ising model with random (+or-J) nearest-neighbour interactions are determined using a numerical transfer matrix method. The calculations are performed on a long strip of width L(3<or=L<or=11) with periodic boundary conditions and finite-size scaling arguments are used to extrapolate to L= infinity . The central result is that the spin-glass correlation length diverges as T- nu at low temperature T with nu =2.59+or-0.13. The heat capacity is similar to the Schottky anomaly. At zero temperature the entropy per spin is 0.0701+or-0.0005 and the internal energy per spin is -(1.4024+or-0.0012)J.

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.