Quantum critical phase diagram of bond alternating Ising model with Dzyaloshinskii-Moriya interaction: signature of ground state fidelity

TL;DR

This paper maps the phase diagram of a bond alternating Ising chain with Dzyaloshinskii-Moriya interaction at zero temperature, identifying quantum phase transitions via fidelity measures and analyzing critical behavior.

Contribution

It introduces a quantum renormalization group approach to evaluate ground state fidelity without prior knowledge of the ground state, revealing critical exponents and phase boundaries.

Findings

Quantum phase transition signatures via fidelity change.

Critical exponent for correlation length divergence is independent of bond alternation.

Maximum helical order varies with bond alternation parameter.

Abstract

We present the zero temperature phase diagram of the bond alternating Ising chain in the presence of Dzyaloshinskii-Moriya interaction. An abrupt change in ground state fidelity is a signature of quantum phase transition. We obtain the renormalization of fidelity in terms of quantum renormalization group without the need to know the ground state. We calculate the fidelity susceptibility and its scaling behavior close to quantum critical point (QCP) to find the critical exponent which governs the divergence of correlation length. The model consists of a long range antiferromagnetic order with nonzero staggered magnetization which is separated from a helical ordered phase at QCP. Our results state that the critical exponent is independent of the bond alternation parameter (lambda) while the maximum attainable helical order depends on lambda.