Critical properties of S=1/2 Heisenberg ladders in magnetic fields

TL;DR

This paper investigates the critical properties of S=1/2 Heisenberg two-leg ladders in magnetic fields using numerical methods, revealing how interchain coupling affects critical exponents and comparing results with experimental data.

Contribution

It provides a detailed numerical analysis of critical exponents in Heisenberg ladders, including effects of diagonal interactions, and compares findings with experimental NMR data.

Findings

Critical exponents depend on interchain coupling sign.

Numerical results align with experimental NMR relaxation rates.

Characteristic behavior of exponents varies with magnetic field and coupling.

Abstract

The critical properties of the $S=1/2$ Heisenberg two-leg ladders are investigated in a magnetic field. Combining the exact diagonalization method and the finite-size-scaling analysis based on conformal field theory, we calculate the critical exponents of spin correlation functions numerically. For a strong interchain coupling, magnetization dependence of the critical exponents shows characteristic behavior depending on the sign of the interchain coupling. We also calculate the critical exponents for the $S=1/2$ Heisenberg two-leg ladder with a diagonal interaction, which is thought as a model Hamiltonian of the organic spin ladder compound ${Cu}_2({1,4-diazacycloheptane})_2{Cl}_4$. Numerical results are compared with experimental results of temperature dependence of the NMR relaxation rate $1/T_1$.