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arXiv:cond-mat/9508104 · Physica Scripta

Thermodynamics of finite quantum systems: application to spin magnetism II

S Sitotaw, Rostislav A. Serota

Published May 1, 1996• 4 citations
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Abstract

We extend our study of thermodynamics of a Kubo particle to temperatures smaller than the mean interlevel spacing. We obtain the distribution functions of spin susceptibility and heat capacity for Poisson and Wigner-Dyson level statistics. We evaluate the line shape of the Knight shift due to spin effects both in a single particle and for the ensemble average and compare it with orbital and spin-orbit contributions.

DOI
10.1088/0031-8949/53/5/003

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We extend our study of thermodynamics of a Kubo particle to temperatures smaller than the mean interlevel spacing. We obtain the distribution functions of spin susceptibility and heat capacity for Poisson and Wigner-Dyson level statistics. We evaluate the line shape of the Knight shift due to spin effects both in a single particle and for the ensemble average and compare it with orbital and spin-orbit contributions.
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Phase transitions for an open system consisting of an ensemble of interacting quantum subsystems with discrete spectrum are studied in the mean-field approximation. In the considered model, the change of an internal symmetry of a thermodynamic system upon the second-order phase transition is due to changing symmetry of distribution of charge/spin density inside each quantum subsystem. The latter can be caused by either splitting of one of lowest degenerated energy level or closing a gap between the levels and appearance of avoided crossing. The effect of external parameters (pressure, field, composition, etc.) results in direct change of internal control parameters: level spacing and/or the strength of interaction between adjacent quantum subsystems. Considering a simplest case of the two-level quantum subsystems, expressions for the free energy as a function of the internal control parameters were obtained in analytical form. The behavior of the heat capacity and susceptibility for different regions of the low-temperature phase diagram including the area of quantum fluctuations was determined.
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and of the equilibrium reduced density matrix of a subsystem for the two different statistics introduced in Part I. In order to analyze their consistency with thermodynamics, these quantities of interest are evaluated in the limit of large number of components of the isolated system. The main results can be summarized as follows: typical values of the entropy and of the equilibrium reduced density matrix as functions of the internal energy in the fixed expectation energy ensemble do not satisfy the requirement of thermodynamics. On the contrary, the thermodynamical description is recovered from the random pure state ensemble (RPSE), provided that one considers systems large enough. The thermodynamic limit of the considered properties for the spin system reveals a number of important features. First canonical statistics (and thus, canonical typicality as long as the fluctuations around the average value are small) emerges without the need of assuming the microcanonical space for the global pure state. Moreover, we rigorously prove (i) the equivalence of the "global temperature," derived from the entropy equation of state, with the "local temperature" determining the canonical state of the subsystems; and (ii) the equivalence between the RPSE typical entropy and the canonical entropy for the overall system.
Abstract In this work, we present a comparative study of thermodynamic quantum equilibrium observables of spin-1 Heisenberg chain. As a theoretical approach, the modified spin-wave theory is chosen. From the numerical side, we consider finite-temperature Lanczos, kernel polynomial, and density matrix renormalization techniques. The results show general consistency of thermodynamic quantities, such as heat capacity and magnetic susceptibility, calculated within the approaches. For the modified spin-wave, the results show some inaccuracy especially at low temperature, failure in capturing the gapped features of spin-1 Heisenberg chain, while the numerical approaches illustrate a good achievement at T→0T\rightarrow 0T→0 T → 0 within the proper parameters chosen.