We consider a two-chain, spin-
21 antiferromagnetic Heisenberg spin ladder in an external magnetic field
H. The spin ladder is known to undergo second-order quantum phase transitions (QPTs) at two critical values
Hc1 and
Hc2 of the magnetic field. There are now known examples of strongly coupled (where the rung exchange interaction is much stronger than the nearest-neighbor intrachain exchange interaction) organic ladder compounds in which QPTs have been experimentally observed. In this paper, we investigate whether well-known bipartite entanglement meaures such as one-site von Neumann entropy, two-site von Neumann entropy, and concurrence develop special features close to the quantum critical points. As suggested by an earlier theorem, the first derivatives of the measures with respect to magnetic field are expected to diverge as $H\ensuremath{\rightarrow}{H}_{c1}$ and $H\ensuremath{\rightarrow}{H}_{c2}$. Based on numerical diagonalization data and a mapping of the strongly coupled ladder Hamiltonian onto the
XXZ chain Hamiltonian, for which several analytical results are known, we find that the derivatives of the entanglement measures diverge as $H\ensuremath{\rightarrow}{H}_{c2}$ but remain finite as $H\ensuremath{\rightarrow}{H}_{c1}$. The reason for this discrepancy is analyzed. We further calculate two recently proposed quantum information theoretic measures, the reduced fidelity and reduced fidelity susceptibility, and show that these measures provide appropriate signatures of the QPTs occuring at the critical points
H=Hc1 and
H=Hc2.
Strong correlations in matter promote a landscape of quantum phases and associated quantum critical points. For metallic systems, there is increasing recognition that the quantum criticality goes beyond the Landau framework and, thus, further means are needed to characterize the quantum critical fluid. Here we do so by studying an entanglement quantity, the quantum Fisher information, in a strange metal system, focusing on the exemplary case of an Anderson/Kondo lattice model near its Kondo destruction quantum critical point. The spin quantum Fisher information peaks at the quantum critical point and indicates a strongly entangled ground state. Our results are supported by the quantum Fisher information extracted from inelastic neutron scattering measurements in heavy fermion metals. Our work elucidates the loss of quasiparticles in strange metals, opens a quantum information avenue to advance the understanding of metallic quantum criticality in a broad range of strongly correlated systems, and points to a regime of quantum matter to realize amplified entanglement. Strange metals exhibit anomalous electronic and thermodynamic properties near a quantum critical point. Here the authors show theoretically that entanglement quantified by quantum Fisher information is amplified in a strange metal at a quantum critical point, which is supported by analysis of experimental data.
The information-Einstein equation states that the information dissipation tensor is a source of spacetime curvature. As the order parameter field approaches a quantum critical point (M→0), two effects occur synergistically—the information dissipation coefficient Υ diverges with power-law scaling 1/x̃^ν, and the geometric back-reaction coefficients diverge as (Λ_op/M)². Together, these constitute the "critical geometric back-reaction enhancement" effect. This paper designs two independent platforms to test this prediction. Platform 1 (superconducting quantum chip) measures the decoherence rate and dissipation noise spectrum near a quantum phase transition critical point. Platform 2 (cold-atom BEC acoustic horizon) measures collective excitation damping near a Feshbach resonance critical point. The two platforms correspond to different universality classes and cross-validate each other. This paper also points out that the high-T_c pseudogap, strange metal linear resistivity, heavy fermion non-Fermi liquid behavior, and 1/f noise universality may be projections of this enhancement in different systems. If both platforms observe divergent signals with scaling exponents consistent with respective universality classes, the information-Einstein equation receives experimental confirmation in the critical region, and the information–geometry closed loop is detected at the laboratory scale for the first time. If the signal is absent, the back-reaction coefficient expansion or the information-Einstein equation needs revision.