The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

TL;DR

This paper investigates the thermodynamics and quantum critical behavior of the spin-1/2 Heisenberg chain, analyzing low-temperature corrections, resolving debates on specific heat, and calculating spin-Peierls exponents under magnetic fields.

Contribution

It provides new numerical and analytical insights into the thermodynamics and critical exponents of the Heisenberg chain, including low-temperature logarithmic corrections and field-dependent spin-Peierls exponents.

Findings

Logarithmic corrections in susceptibility and specific heat at extremely low temperatures.

Resolution of a longstanding controversy regarding the specific heat.

Calculation of the spin-Peierls exponent as a function of magnetic field.

Abstract

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures ($T/J=10^{-24}$) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.