Critical Properties of gapped spin-1/2 chains and ladders in a magnetic field

TL;DR

This paper investigates the critical properties of gapped spin-1/2 chains and ladders under magnetic fields, analyzing phase transitions, critical exponents, and dynamical susceptibilities to understand their low-temperature behavior.

Contribution

It provides a comprehensive calculation of critical exponents and dynamical susceptibilities for gapped spin-1/2 systems in magnetic fields, including special cases like dimerized and frustrated chains.

Findings

Critical exponents at the transition point $H_{c1}$ are determined.

Dynamical susceptibilities at finite temperature are computed.

Low-temperature behavior of nuclear spin relaxation rate $T_1^{-1}$ is analyzed.

Abstract

An interesting feature of spin-1/2 chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field $H$. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field $H_{c1}$ and an upper critical field $H_{c2}$, where it is gapless and has power law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field $H_{c1}$ and in its vicinity. Our analysis also applies to the spin-1/2 ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low temperature behaviour of the nuclear spin relaxation rate $T_1^{-1}$. We discuss the results obtained here for the special cases of the dimerised chain, frustrated chain and the spin-1/2 ladder.