We investigate thermodynamic properties like specific heat c V and susceptibility χ in anisotropic J 1 – J 2 triangular quantum spin systems ( ). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to N = 28 sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on c V ( T ) and . We show the variation of peak position and peak height of these quantities as function of control parameter . We demonstrate that maximum peak positions and heights in Néel phase and spiral phases are strongly asymmetric, much more than in the square lattice J 1 – J 2 model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs 2 CuCl 4 and Cs 2 CuBr 4 from our FTLM results.
We investigate thermodynamic properties like specific heat c V and susceptibility χ in anisotropic J 1 – J 2 triangular quantum spin systems ( ). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to N = 28 sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on c V ( T ) and . We show the variation of peak position and peak height of these quantities as function of control parameter . We demonstrate that maximum peak positions and heights in Néel phase and spiral phases are strongly asymmetric, much more than in the square lattice J 1 – J 2 model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs 2 CuCl 4 and Cs 2 CuBr 4 from our FTLM results.
We study the S=1/2 anisotropic Heisenberg antiferromagnet on finite triangular lattices with N\ensuremath{\le}24 sites: H=2JJ〈i,j〉(SixSjx +SiySjy +\ensuremath{\Delta}SizSjz) with 0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1. The specific heat C and the chiral-order parameter 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 are calculated using a quantum transfer Monte Carlo method. Remarkable differences in the size dependences of C and 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 are found between the cases of \ensuremath{\Delta}\ensuremath{\le}0.4 and of \ensuremath{\Delta}\ensuremath{\ge}0.6. For \ensuremath{\Delta}\ensuremath{\le}0.4, the peak height of C increases with increasing N and an extrapolation of 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 to the thermodynamic limit gives a finite, nonzero value at low temperatures. In contrast with these, for \ensuremath{\Delta}\ensuremath{\ge}0.6, the peak height does not increase and the extrapolation of 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 gives a smaller value even at very low temperatures indicating the absence of a long-range chiral order. From the results, we suggest that the chiral-ordered phase transition occurs at a finite, nonzero temperature when \ensuremath{\Delta}\ensuremath{\le}${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$ with ${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$\ensuremath{\gtrsim}0.4. The phase diagram of the model is predicted.
Abstract We study the temperature dependence of the thermodynamic properties of spin-1/2 antiferromagnets on two-dimensional lattices. Our analysis employs the sine-square deformation (SSD), in which a real-space envelope function is applied to the Hamiltonian so that the local energy scale is smoothly reduced to zero at the system boundaries. The quantum eigenstates of the SSD Hamiltonian exhibit bulk-like behavior near the system center, effectively mimicking the thermodynamic limit even in small finite-size calculations. Using these fictitious bulk states, we compute the energy density, specific heat, and magnetic susceptibility as functions of temperature. We find that both the triangular- and kagome-lattice antiferromagnets show either a shoulder or a pronounced double-peak structure in the low-temperature specific heat, whereas the kagome case particularly shows a strong enhancement of magnetic susceptibility down to the lowest temperature range. These direct comparisons, together with the square-lattice and one-dimensional cases, reveal that although both frustrated systems retain a substantial amount of entropy, the low-energy excitations below ∼ 0.5 J ∼0.5J of the kagome lattice are predominantly governed by the magnetic excited states, whereas not much for the triangular lattice.
Abstract Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.
Thermodynamic properties, specific heat and magnetic susceptibility, of spin-1/2 Ising-like Heisenberg model are investigated by an exact diagonalization method for small finite size kagome- and triangular-lattices up to 18-spins. The enhancement of magnetic susceptibility from the Curie–Weiss law and the peaks-structure of specific heat, rather generally detected experimentally in triangle-based spin systems including herbertsmithite, are interpreted as an intrinsic property of triangle-based frustrated spin systems with some extent of exchange anisotropy and are inferred as owing to a quantum-classical crossover.
We study the S= quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins N\ensuremath{\leqslant}27, and those at finite temperatures using a quantum transfer Monte Carlo method for N\ensuremath{\leqslant}24. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3 plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic-field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin-flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.
The spin-1/2 anisotropic triangular model, which is believed to describe the materials Cs2CuCl4 and Cs2CuBr4, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper, we use twisted boundary conditions and exact diagonalization techniques to study the ground state of this model as a function of exchange parameter strength. With these boundary conditions we are able to extract the inter- and intrachain ordering q vectors for the $\frac{{J}^{\ensuremath{'}}}{J}<1$ region finding very close agreement with recent DMRG results on much larger systems. Our results suggest a phase transition between a long-range incommensurate spiral ordered phase, and a more subtle phase with short-range spiral correlations with the q vector describing the incommensurate correlations varying smoothly through the transition. In the latter phase correlations between next-nearest chains exhibit an extremely close competition between predominantly antiferromagnetic and ferromagnetic correlations. Further analysis suggests that the antiferromagnetic next-nearest chain correlations may be slightly stronger than the ferromagnetic ones. This difference is found to be slight but in line with previous renormalization group predictions of a collinear antiferromagnetic ordering in this region.