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arXiv:cond-mat/0405578 · Physical Review B

Exact low-temperature behavior of a kagomé antiferromagnet at high fields

Mike E. Zhitomirsky, Hirokazu Tsunetsugu

Published Sep 16, 2004• 171 citations
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Abstract

Low-energy degrees of freedom of a spin-$1∕2$ kagom\'e antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows us to obtain the quantitative description of the magnetothermodynamics of a quantum kagom\'e antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.

DOI
10.1103/physrevb.70.100403

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Low-energy degrees of freedom of a spin-1∕21∕21∕2 kagom'e antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows us to obtain the quantitative description of the magnetothermodynamics of a quantum kagom'e antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.
The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band.The corresponding excitations can be localized on loops in real space and have been coined "localized magnons".Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them.Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice.We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations.The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field.We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM).For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures.
We consider the S = 1 / 2 antiferromagnetic Heisenberg model on a frustrated kagome-lattice bilayer with strong nearest-neighbor interlayer coupling and examine its low-temperature magnetothermodynamics using a mapping onto a rhombi gas on the kagome lattice. Besides, we use finite-size numerics to illustrate the validity of the classical lattice-gas description. Among our findings there are (i) the absence of an order-disorder phase transition and (ii) the sensitivity of the specific heat at low temperatures to the shape of the system just below the saturation magnetic field even in the thermodynamic limit.
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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.
For a class of highly frustrated antiferromagnetic quantum spin lattices the ground state exhibits a huge degeneracy in high magnetic fields due to the existence of localized magnon states. For some of these spin lattices (in particular, the 1D dimer-plaquette, sawtooth and kagom\'elike chains as well as the 2D kagom\'e lattice) we calculate rigorously the ground-state entropy at the saturation field. We find that the ground-state entropy per site remains finite at saturation. This residual ground-state entropy produces a maximum in the field dependence of the isothermal entropy at low temperatures. By numerical calculation of the field dependence of the low-temperature entropy for the sawtooth chain we find that the enhancement of isothermal entropy is robust against small deviations in exchange constants. Moreover, the effect is most pronounced in the extreme quantum case of spin 12\frac{1}{2}21​.