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Quantum spin system with on-site exchange in a magnetic field

Grzegorz Pawłowski

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

We present the results of a full diagonalisation applied to a 1 D quantum spin system with on-site exchange anisotropy. The model considered is a quantum generalization of the 1 D classical Blume–Capel model. Thermodynamic properties of the system in the presence of magnetic field are examined taking into account a quantum spin ladder with a periodic boundary condition, where each rung of the ladder contains two interacting spins –1/2. This effective spin –1 system exhibits very rich thermodynamic behaviour. We present the ground state results, showing many various types of magnetic configurations and compare it with the classical case. The calculations are performed in the unified simulation environment ALPS, which offers the fulldiag application.

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We present the results of a full diagonalisation applied to a 1 D quantum spin system with on-site exchange anisotropy. The model considered is a quantum generalization of the 1 D classical Blume–Capel model. Thermodynamic properties of the system in the presence of magnetic field are examined taking into account a quantum spin ladder with a periodic boundary condition, where each rung of the ladder contains two interacting spins –1/2. This effective spin –1 system exhibits very rich thermodynamic behaviour. We present the ground state results, showing many various types of magnetic configurations and compare it with the classical case. The calculations are performed in the unified simulation environment ALPS, which offers the fulldiag application.
The effects of multispin interactions upon quantum spin ladders are investigated theoretically. A two-leg S=12S=\frac{1}{2}S=21​ quantum spin ladder is taken to have intrarung (inter-rung) quadratic (biquadratic) Heisenberg exchange-type interactions and is placed in a uniform magnetic field. Due to the commutability properties of the Hamiltonian, the magnetic canonical partition function of the model is exactly calculable by a method of rung transfer matrix. Exact solutions are then derived for thermodynamic quantities like free and internal energies, magnetization, and magnetic susceptibilities (initial and nonlinear). The zero-temperature results comprise exact solutions in the complete interaction parameter space for the ground-state energy and degeneracy, zero-field spin gap, loci of quantum phase transitions, and the critical magnetic field.
In this work, we investigate the thermodynamic properties of the quantum Blume-Capel model with spin S=5/2 S = 5/2 S=5/2 in the presence of transverse and random crystalline fields. The system is described by a Hamiltonian that includes ferromagnetic exchange interactions between nearest neighbors, a longitudinal single-ion anisotropy, and a transverse single-ion anisotropy. Using a mean-field approach based on Bogoliubov's inequality for the Gibbs free energy, we derive the fundamental thermodynamic potential and the equation of state for the magnetization. The influence of the longitudinal and transverse anisotropy parameters on the magnetic ordering and phase transitions is analyzed in detail. We present magnetization versus temperature diagrams for various combinations of the anisotropies, exploring both positive and negative values. Our results reveal that the system exhibits standard second-order phase transitions for most parameter ranges, with no evidence of tricritical behavior. However, for certain positive values of the anisotropies, the model displays a first-order phase transition within the ordered phase, characterized by a jump from a higher-spin ordered state to a lower-spin ordered state. The critical temperatures are shown to be sensitive to the magnitude and sign of the anisotropy parameters. In particular, negative transverse anisotropies favor magnetic order, raising the critical temperature, while positive anisotropies promote disorder, lowering the critical temperature. This study provides a comprehensive analysis of the phase diagram of the S=5/2 S = 5/2 S=5/2 quantum Blume-Capel model and highlights the role of transverse fields in modifying the critical behavior.
Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.
The magnetic and thermodynamic properties of the Blume-Capel model are investigated within an approach combined with quantum mechanics and mean-field approximation for the spin-1/2 and spin-1 with coordination number z = 3. The spin-1 sites are subjected to transverse crystal fields Dx and Dy. In addition, the bilinear interaction parameter J is randomly distributed with an adjustable parameter α>0 such that certain sites are under the influence of αJ with probability p while the rest are subject to J with probability 1−p. The thermal behaviors of the order parameters have been studied to determine the nature of phase transitions and to calculate phase diagrams in the (Dx,kT), (Dy,kT), (α,kT), (|J|,kT), and (p,kT) planes. The obtained results revealed a rich variety of critical phenomena including first- and second-order phase transitions, tricritical points, and compensation temperatures. Under an external magnetic field, the system exhibits both simple and multi-hysteresis behaviors. Furthermore, the coercive field and remanent magnetization decrease with increasing temperature.
The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.