Article

# Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields

• ##### Taras Krokhmalskii
Physical review. B, Condensed matter (Impact Factor: 3.77). 07/2006; DOI: 10.1103/PhysRevB.74.144430
Source: arXiv

ABSTRACT We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-)temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.

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• ##### Article: Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario
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ABSTRACT: We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain and the two-dimensional square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic fields, we construct low-energy effective Hamiltonians which are much simpler than the initial ones. These effective Hamiltonians allow a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory we also use a localized-magnon based approach leading to a substantial improvement of the strong-coupling approximation. We perform extensive exact diagonalization calculations to check the quality of different effective Hamiltonians by comparison with the initial models. Based on the effective-model description we examine the low-temperature properties of the considered frustrated quantum Heisenberg antiferromagnets in the high-field regime. We also apply our approach to explore thermodynamic properties for a generalized diamond spin chain model suitable to describe azurite at high magnetic fields. Interesting features of these highly frustrated spin models consist in a steep increase of the entropy at very small temperatures and a characteristic extra low-temperature peak in the specific heat. The most prominent effect is the existence of a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition occurring in the two-dimensional model.
Physical review. B, Condensed matter 04/2013; 88(9). · 3.77 Impact Factor
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##### Article: The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond
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ABSTRACT: We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in a $z$-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.
12/2013;
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##### Article: Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
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ABSTRACT: 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 {\em 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 $\mu_0$. 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. Comment: 20 pages, 12 figures, 2 tables
Physical Review B 01/2010; 81(1):014421. · 3.66 Impact Factor

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