Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D Regime

Abstract

We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of $\sim 0.6$. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of ${\mathrm{Cs}}_2{\mathrm{CuBr}}_4$ and ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.

References in corpus (17)

• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
• Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
• Observation of extended scattering continua characteristic of spin fractionalization in the 2D frustrated quantum magnet Cs2CuCl4 by neutron scattering
• Direct Measurement of the Spin Hamiltonian and Observation of Condensation of Magnons in the 2D Frustrated Quantum Magnet Cs2CuCl4
• Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
• Spinons and triplons in spatially anisotropic frustrated antiferromagnets
• Bose-Einstein Condensation of Magnons in Cs2CuCl4
• Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions
• Possibility of Gapless Spin Liquid State by One-dimensionalization
• Exact renormalization group for quantum spin systems
• Specific Heat Study of 1D and 2D Excitations in the Layered Frustrated Quantum Antiferromagnets Cs${}_2$CuCl${}_{4-x}$Br${}_x$
• Nonlinear spectra of spinons and holons in short GaAs quantum wires
• Hierarchy of modes in an interacting system
• Nature of the many-body excitations in a quantum wire: theory and experiment
• Spectral edge mode in interacting one-dimensional systems
• Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions