A comparative study of quantum resources in bipartite Lipkin–Meshkov–Glick model under DM interaction and Zeeman splitting

Abstract We assess the thermal resilience of key quantum resources-( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mrow> <m:mi>ℓ</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> </m:math> {\ell }_{1} )-norm coherence ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>Q</m:mi> </m:mrow> </m:math> Q ), quantum discord ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>D</m:mi> </m:mrow> </m:math> D ), logarithmic negativity ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">ℒN</m:mi> </m:mrow> </m:math> {\mathcal{ {\mathcal L} N}} ), Bell nonlocality ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">ℬ</m:mi> </m:mrow> </m:math> {\mathcal{ {\mathcal B} }} ), and quantum steering ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">S</m:mi> </m:mrow> </m:math> {\mathcal{S}} )-in a bipartite Lipkin–Meshkov–Glick (LMG) spin system subject to competing Dzyaloshinskii–Moriya (DM) interactions and Zeeman splitting. By varying temperature ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>T</m:mi> </m:mrow> </m:math> T ), spin–spin coupling ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>λ</m:mi> </m:mrow> </m:math> \lambda ), magnetic field strength ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mrow> <m:mi>B</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:mrow> </m:math> {B}_{0} ), and DM amplitude ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mrow> <m:mi>D</m:mi> </m:mrow> <m:mrow> <m:mi>z</m:mi> </m:mrow> </m:msub> </m:mrow> </m:math> {D}_{z} ), we reveal a clear hierarchy of thermal stability: coherence and discord remain robust well beyond the temperatures at which nonlocality ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">ℬ</m:mi> </m:mrow> </m:math> {\mathcal{ {\mathcal B} }} ), steering ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">S</m:mi> </m:mrow> </m:math> {\mathcal{S}} ), and bipartite entanglement ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">ℒN</m:mi> </m:mrow> </m:math> {\mathcal{ {\mathcal L} N}} ) undergo successive thermal collapse. Stronger spin–spin c