Quantum Fisher Information (QFI) is a ubiquitous quantity with applications ranging from quantum metrology and resource theories to condensed matter physics. In equilibrium local quantum many-body systems, the QFI of a subsystem with respect to an extensive observable is typically proportional to the subsystem's volume. Specifically, in large subsystems at equilibrium, the QFI per unit volume squared becomes negligible. We reveal a natural mechanism that amplifies the QFI in a quantum spin chain with a zero-temperature ordered phase. At zero or sufficiently low temperatures, a transient localized perturbation enhances the QFI, causing it to scale quadratically with the subsystem's length. Furthermore, this enhancement can be controlled through more general localized kicking protocols. We also revisit the behavior of the quantum Fisher information after a global quench in the thermodynamic limit, focusing on the generation of localized -- confined within compact subsystems -- multipartite entanglement. We show that the density of localized multipartite entanglement approaches zero at late times, but there is an optimal time frame proportional to the length in which subsystems fall into macroscopic quantum states. We test our predictions against numerical data obtained using a novel technique, based on a remarkable identity between quantum Fisher information and Wigner-Yanase-Dyson skew information, that allows one to compute the quantum Fisher information with respect to the order parameter in noninteracting spin chains.
Quantum Fisher Information (QFI) is a ubiquitous quantity with applications ranging from quantum metrology and resource theories to condensed matter physics. In equilibrium local quantum many-body systems, the QFI of a subsystem with respect to an extensive observable is typically proportional to the subsystem's volume. Specifically, in large subsystems at equilibrium, the QFI per unit volume squared becomes negligible. We reveal a natural mechanism that amplifies the QFI in a quantum spin chain with a zero-temperature ordered phase. At zero or sufficiently low temperatures, a transient localized perturbation enhances the QFI, causing it to scale quadratically with the subsystem's length. Furthermore, this enhancement can be controlled through more general localized kicking protocols. We also revisit the behavior of the quantum Fisher information after a global quench in the thermodynamic limit, focusing on the generation of localized -- confined within compact subsystems -- multipartite entanglement. We show that the density of localized multipartite entanglement approaches zero at late times, but there is an optimal time frame proportional to the length in which subsystems fall into macroscopic quantum states. We test our predictions against numerical data obtained using a novel technique, based on a remarkable identity between quantum Fisher information and Wigner-Yanase-Dyson skew information, that allows one to compute the quantum Fisher information with respect to the order parameter in noninteracting spin chains.
Symmetry breaking underlies diverse phenomena from phase transitions in condensed matter to fundamental interactions in gauge theories. Despite many proposed indicators, a general quantification of symmetry breaking that is faithful, computable, and valid in the thermodynamic limit has remained elusive. Here, within quantum resource theory, we propose the quantum Fisher information (QFI) as such a measure. We demonstrate its utility by computing QFI for paradigmatic models: in the BCS superconductor, the QFI counts the number of Cooper pairs; in the transverse-field XY spin chains, it captures topological phase transition that has no local order parameter; and in quantum quench dynamics, it allows us to exactly derive the microscopic origin and conditions of the quantum Mpemba effect in terms of excitation propagation, including in the thermodynamic limit--beyond the reach of previous analyses. Our results show that the QFI, which is a complete resource monotone in the resource theory of asymmetry that plays the role of entanglement entropy in entanglement theory, faithfully captures symmetry breaking in condensed-matter systems. These results highlight the QFI as a universal and physically meaningful diagnostic of symmetry breaking in both equilibrium and non-equilibrium quantum many-body systems.
In this paper, we study the ground-state quantum Fisher information (QFI) in one-dimensional spin-1 models, as witness to multipartite entanglement. The models addressed are the bilinear-biquadratic model, the most general isotropic SU(2)-invariant spin-1 chain, and the XXZ spin-1 chain, both with nearest-neighbor interactions and open boundary conditions. We show that the scaling of the QFI of strictly nonlocal observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scales maximally. Analyzing its behavior at the critical phases, we are also able to recover the scaling dimensions of the order parameters, both for local and string observables. The numerical results have been obtained by exploiting the density-matrix renormalization-group algorithm and tensor network techniques.
Quantum Fisher information in a quenched p+ip superfluid
The quantum Fisher information (QFI) is widely used to characterize quantum phases and transitions, but its diagnostic power sometimes relies on selecting special generators based on prior knowledge of the underlying physics. We ask whether this requirement can be relaxed in nonequilibrium systems by studying the QFI of the long-time asymptotic state of a two-dimensional p+ip superfluid following an instantaneous quench of the coupling strength, using the particle number within a large subextensive subsystem as the generator. In equilibrium, the ground-state QFI is continuous across the topological transition between the weak-pairing BCS and the strong-pairing BEC phases, showing no direct signature of the transition. After the quench, however, the QFI associated with the same generator distinguishes the three dynamical phases and can encode the topology of the pre-quench state. In phase I, with a vanishing order parameter, the QFI Fourier spectrum consists of a single zero-frequency spike determined by the nonequilibrium distribution function. In phase II, with a constant nonzero order parameter, the QFI spectrum contains a zero-frequency spike and two continua separated by a gap set by the minimum asymptotic quasiparticle energy. The continuum edge behavior reveals whether this minimum occurs at zero or finite momentum. In the former case, the spectral weight vanishes at the edge, with the sign just inside the continuum encoding the pre-quench topology for large subsystem. In phase III, with a time-periodic order parameter, the QFI spectrum exhibits discrete peaks at integer multiples of the oscillation frequency, together with continua associated with the Floquet quasienergy spectrum. Our results show that driving the system out of equilibrium can enhance the diagnostic power of the QFI for a standard physical observable, revealing information inaccessible in equilibrium.
Abstract We study the multipartite entanglement of a quantum many-body system undergoing a quantum quench. We quantify the multipartite entanglement through the quantum Fisher information (QFI) density, and we are able to express it after a quench in terms of a generalised response function. For pure state initial conditions and in the thermodynamic limit, we can express the QFI as the fluctuations of an observable computed in the so-called diagonal ensemble. We apply the formalism to the dynamics of a quantum Ising chain, after a quench in the transverse field. In this model the asymptotic state is, in almost all cases, more than two-partite entangled. Moreover, starting from the ferromagnetic phase, we find a divergence of multipartite entanglement for small quenches closely connected to a corresponding divergence of the correlation length.
Abstract The theory of multipartite entanglement provides a robust framework for understanding complex phenomena in quantum many-body systems, while multipartite entanglement also serves as a key resource in numerous quantum information processing tasks. Using density matrix renormalization group calculations, we study the multipartite entanglement in one-dimensional quantum long-range ferromagnetic and antiferromagnetic Ising chains with algebraically decaying interactions 1/ r α , respectively. To quantitatively probe the system’s multipartite entanglement structure, we employ the quantum Fisher information (QFI). Our results reveal two key behaviors: as the system size increases, the QFI rises, while the multipartite entanglement density decreases and converges toward a constant value. The latter trend points to a fundamental constraint on entanglement distribution in the thermodynamic limit. We further discuss the effects of the magnetic field and the exponent α on the QFI. We find that the peak values of the QFI increase with increasing α . Additionally, the discontinuity in the QFI can be regarded as a powerful tool for characterizing quantum phase transitions in the systems.
The dynamics of relative entropy and l1 norm of coherence, as well as, the Wigner-Yanase skew and quantum Fisher information are studied in the one-dimensional XY spin chain in the presence of a time-dependent transverse magnetic field. We show that, independent of the initial state of the system and while the relative entropy of coherence, the l1 norm of coherence, and quantum Fisher information are incapable, surprisingly, the Wigner-Yanase skew information dynamic can truly spotlight the equilibrium critical point. We also observe that, when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent of the initial phase of the system. This is the promised universality of the first suppression (revival) time.