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Register a new userLogarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model
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Added by
Mat\\'ias Gabriel Gonzalez
Publication date
2021
fields
Physics
and research's language is
English
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We present an interpolation method for the specific heat $c_v(T)$, when there is a phase transition with a logarithmic singularity in $c_v$ at a critical temperature $T=T_c$. The method uses the fact that $c_v$ is constrained both by its high temperature series expansion, and just above $T_c$ by the type of singularity. We test our method on the ferro and antiferromagnetic Ising model on the two-dimensional square, triangular, honeycomb, and kagome lattices, where we find an excellent agreement with the exact solutions. We then explore the XXZ Heisenberg model, for which no exact results are available.
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We present new results for the Kondo lattice model of strongly correlated electrons, in 1-, 2-, and 3-dimensions, obtained from high-order linked-cluster series expansions. Results are given for varies ground state properties at half-filling, and for spin and charge excitations. The existence and nature of the predicted quantum phase transition are explored.
The bond-propagation (BP) algorithm for the specific heat of the two dimensional Ising model is developed and that for the internal energy is completed. Using these algorithms, we study the critical internal energy and specific heat of the model on the square lattice and triangular lattice with free boundaries. Comparing with previous works [X.-T. Wu {it et al} Phys. Rev. E {bf 86}, 041149 (2012) and Phys. Rev. E {bf 87}, 022124 (2013)], we reach much higher accuracy ($10^{-26}$) of the internal energy and specific heat, compared to the accuracy $10^{-11}$ of the internal energy and $10^{-9}$ of the specific heat reached in the previous works. This leads to much more accurate estimations of the edge and corner terms. The exact values of some edge and corner terms are therefore conjectured. The accurate forms of finite-size scaling for the internal energy and specific heat are determined for the rectangle-shaped square lattice with various aspect ratios and various shaped triangular lattice. For the rectangle-shaped square and triangular lattices and the triangle-shaped triangular lattice, there is no logarithmic correction terms of order higher than 1/S, with S the area of the system. For the triangular lattice in rhombus, trapezoid and hexagonal shapes, there exist logarithmic correction terms of order higher than 1/S for the internal energy, and logarithmic correction terms of all orders for the specific heat.
A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range order (LRO) and short-range order (SRO) at arbitrary temperatures. The magnetization, Neel temperature T_N, specific heat, and uniform static spin susceptibility $chi$ are calculated self-consistently. As the main result, we obtain LRO at finite temperatures in two dimensions, where the dependence of T_N on the compass-model interaction is studied. We find that T_N is close to the experimental value for Ba2IrO4. The effects of SRO are discussed in relation to the temperature dependence of $chi$.
The Hund coupling in multiorbital Hubbard systems induces spin freezing and associated Hund metal behavior. Using dynamical mean field theory, we explore the effect of local moment formation, spin and charge excitations on the entropy and specific heat of the three-orbital model. In particular, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase at low temperatures, and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. We also clarify how these temperature scales depend on the interaction parameters and filling.
We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the $S = 1$ Heisenberg antiferromagnet with easy-axis or easy-plane single site anisotropy, on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared with spin-wave theory.
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