Quantum versus classical behavior in the boundary susceptibility of the ferromagnetic Heisenberg chain

Abstract

We calculate the temperature dependence of the boundary susceptibility ${\chi }_B$ for the quantum ferromagnetic Heisenberg chain by a modified spin-wave theory (MSWT). We find that ${\chi }_B$ diverges at low temperatures $\sim -T^{-3}$ and therefore more rapidly and with opposite sign than the bulk susceptibility ${\chi }_{\text{bulk}}\sim T^{-2}$. Our result for ${\chi }_B$ is identical in leading order with the result for the classical system. In next leading orders, however, quantum corrections to the classical result exist which are important to obtain a good description over a wide temperature range. For the $S=1/2$ case, we show that our full result from MSWT is in excellent agreement with numerical data obtained by the density-matrix renormalization group applied to transfer matrices. Finally, we discuss the quantum to classical crossover as well as consequences of our results for experiment in some detail.

arXiv comment6 pages, 3 figures

References in corpus (11)

• Density matrix renormalisation group for a quantum spin chain at non-zero temperature
• Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method
• Green's-function theory of the Heisenberg ferromagnet in a magnetic field
• Boundary susceptibility in the spin-1/2 chain: Curie like behavior without magnetic impurities
• Temperature driven crossover phenomena in the correlation lengths of the one-dimensional t-J model
• Boundary contributions to specific heat and susceptibility in the spin-1/2 XXZ chain
• Impurity corrections to the thermodynamics in spin chains using a transfer-matrix DMRG method
• Universal low-temperature properties of quantum and classical ferromagnetic chains
• Surface free energy for systems with integrable boundary conditions
• Boundary susceptibility in the open XXZ-chain
• Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field,

Cited by in corpus (6)

• Correlation functions of the open XXZ chain I
• Correlation functions of the open XXZ chain II
• The J1-J2 Heisenberg model at and close to its z=4 quantum critical point
• The dimerized ferromagnetic Heisenberg chain
• Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
• Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction