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Physical Review B

Quantum phase transition in a solvable spin model

Ping Lou

Published Aug 18, 2005• 17 citations
Publisher

Abstract

The spin- $\frac{1}{2}XX$ chain with three-spin and uniform long-range interactions among the $z$ components of the spins is investigated. Using the Jordan-Wigner transformation, the thermodynamic quantities and spin transports of the model are evaluated exactly. The phase diagram together with the key parameters characterizing quantum phase transitions is presented.

DOI
10.1103/physrevb.72.064435

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Abstract A spin‐½ XX chain with three‐spin and uniform long‐range interactions among the z components of the spins is constructed. Based upon the model, using the Jordan–Wigner transformation, the thermodynamic quantities and spin transports of the system are evaluated exactly. The phase diagram together with the key parameters characterizing quantum phase transitions is presented. It is noted that, similarly to classical first‐order phase transitions, there are also the metastable states “supercooled” and “superheated” in the first‐order quantum phase transitions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The quantum phase transition in the spin-12\frac{1}{2}21​ XX Heisenberg chain model with three-spin interaction is studied. Using the Jordan-Wigner transformation, several thermodynamic, as well as thermal and spin transport quantities of the system are calculated exactly. It is shown that the three-spin interaction influences the calculated quantities and leads to characteristic features of the quantum phase transition. The effects of a finite magnetic field on the magnetic moment and magnetic susceptibility are also discussed.
The one-dimensional spin-1/2 Heisenberg XXZ ferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field was studied by using the mean-field Jordan-Wigner transformation.The analytic expressions and the numerical results of the thermodynamic quantities,including the Helmholtz free energy,internal energy,specific heat,magnetization and isothermal susceptibility,were obtained.We also discussed the phase transitions of the system at a finite temperature.Our results agreed with that from other literatures in the degenerate condition.
Using the mean-field Jordan-Wigner transformation,this paper studies the one-dimensional spin-Heisenberg XYZ antiferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field.The research has obtained such analytic expressions and the numerical results of the thermodynamic quantities,as the Helmholtz free energy,internal energy,specific heat,magnetization and susceptibility.The results in the degenerate condition agree with that from other literatures
This chapter is devoted to a discussion of quantum phase transitions in regularly alternating spin-1/2 Ising chain in a transverse field. After recalling some generally-known topics of the classical (temperature-driven) phase transition theory and some basic concepts of the quantum phase transition theory I pass to the statistical mechanics calculations for a one-dimensional spin-1/2 Ising model in a transverse field, which is the simplest possible system exhibiting the continuous quantum phase transition. The essential tool for these calculations is the Jordan-Wigner fermionization. The latter technique being completed by the continued fraction approach permits to obtain analytically the thermodynamic quantities for a `slightly complicated' model in which the intersite exchange interactions and on-site fields vary regularly along a chain. Rigorous analytical results for the ground-state and thermodynamic quantities, as well as exact numerical data for the spin correlations computed for long chains (up to a few thousand sites) demonstrate how the regularly alternating bonds/fields effect the quantum phase transition. I discuss in detail the case of period 2, swiftly sketch the case of period 3 and finally summarize emphasizing the effects of periodically modulated Hamiltonian parameters on quantum phase transitions in the transverse Ising chain and in some related models.