The idea of quantum texture has been recently proposed and used as a tool for quantifying coherences and for quantum gate identification. In this work we offer a study on its usage to quantum phase transitions, demonstrating the rugosity metric as a simple tool for effective phase-transition probing. We establish the link between rugosity in the computational basis and the hierarchy of spin correlators, and analyze rugosities defined in the global ground-state and in ground-states belonging to different magnetization sectors (to which we refer to as global vs symmetry-resolved rugosities) to study the phase diagram of the Heisenberg XXZ model. We find distinct rugosity signatures at both transition points. In particular, a sharp feature appears at $Δ=1$ already for small systems, revealing a pronounced sensitivity of the correlation hierarchy encoded by the texture to this point. Since the BKT transition coincides with the isotropic $SU(2)$ point of the XXZ model, this behavior may reflect a particular sensitivity of rugosity to the structure of the spin-correlation hierarchy at isotropy.
The idea of quantum texture has been recently proposed and used as a tool for quantifying coherences and for quantum gate identification. In this work we offer a study on its usage to quantum phase transitions, demonstrating the rugosity metric as a simple tool for effective phase-transition probing. We establish the link between rugosity in the computational basis and the hierarchy of spin correlators, and analyze rugosities defined in the global ground-state and in ground-states belonging to different magnetization sectors (to which we refer to as global vs symmetry-resolved rugosities) to study the phase diagram of the Heisenberg XXZ model. We find distinct rugosity signatures at both transition points. In particular, a sharp feature appears at Δ=1 already for small systems, revealing a pronounced sensitivity of the correlation hierarchy encoded by the texture to this point. Since the BKT transition coincides with the isotropic SU(2) point of the XXZ model, this behavior may reflect a particular sensitivity of rugosity to the structure of the spin-correlation hierarchy at isotropy.
We investigate the role of quantum state texture in dynamical quantum phase transitions by establishing a direct connection between critical nonequilibrium dynamics and the recently introduced notion of rugosity, a measure of quantum state texture. Considering a generic quench protocol, we analyze both standard formulations of dynamical quantum phase transitions. For type-I transitions, characterized through the long-time behavior of a dynamical order parameter, we show that the time-averaged rugosity, evaluated in the eigenbasis of the pre-quench Hamiltonian, exhibits an order-parameter-like behavior across the transition. In the Lipkin-Meshkov-Glick model, this behavior is traced back to the underlying semiclassical structure, where crossing the excited-state quantum phase transition separatrix controls the redistribution of the quantum state over the pre-quench energy basis. We further demonstrate that the response function associated with the time-averaged rugosity develops a pronounced critical peak whose maximum grows algebraically with the system size, providing quantitative finite-size evidence of its sensitivity to the dynamical critical point. For type-II transitions, characterized by nonanalyticities in the Loschmidt rate function, we establish an exact connection with rugosity. For a suitable choice of basis, the rate function is exactly given by the density of rugosity, establishing a model-independent equivalence. Moreover, we show that even in physically motivated bases, such as the pre-quench energy eigenbasis, rugosity provides clear signatures of dynamical criticality. Our results establish rugosity as a sensitive probe of dynamical quantum phase transitions while highlighting its role as a basis-dependent measure of quantum state texture, thereby providing an information-theoretic perspective on nonequilibrium quantum critical phenomena.
We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.
In this study we investigate the ground-state phase diagram of the quantum spin-1/2 anisotropic XZ chain using the infinite time-evolving block decimation algorithm. The model exhibits four distinct phases: FM_{x}, FM_{z}, AFM_{z}, and PM. In terms of the transverse magnetic field h and anisotropy parameter J, our analysis focuses on the lines h=0 and 0.5 with J≥0, where different types of quantum phase transitions (QPTs) occur. We compute the bifurcation behavior of the ground-state fidelity per lattice site. On the line h=0, continuous behavior at the bifurcation point identifies a continuous QPT between the ordered FM_{x} and FM_{z} phases at the critical point J_{c1}, with bifurcations on both sides reflecting Z_{2} symmetry breaking in both phases. On the line h=0.5, a continuous bifurcation indicates a QPT between the ordered FM_{x} and disordered PM phases at J_{c2}, with bifurcation occurring only on one side, corresponding to Z_{2} symmetry breaking in a single phase. We further compute the ground-state fidelity susceptibility per lattice site. When the ground state is obtained from random initial states, the fidelity susceptibility exhibits oscillatory behavior in the symmetry-broken phase, providing a clear signature of ground-state degeneracy. These fidelity-based measures serve as effective tools for identifying critical points and characterizing the nature of symmetry breaking. To complement these results, we evaluate the two-spin Wigner-Yanase skew information and local quantum uncertainty (LQU) as indicators of quantum correlations. While both detect QPTs, we find that not all nonanalytic features in the LQU correspond to genuine phase transitions. A critical behavior analysis is carried out at J_{c1} and J_{c2} to extract the critical exponents η^{I}, η^{C}, η^{x}, and η^{z}, associated with mutual information I(r), classical correlation C(r), and spin-spin correlations 〈σ_{i}^{x}σ_{j}^{x}〉, 〈σ_{i}^{z}σ_{j}^{z}〉. Our results demonstrate that η^{I}=η^{C} and η^{x/z}=η^{α}/2 for α=I,C, consistent with known universal scaling relations. We also extract the order parameter exponent β, correlation length exponent ν, dynamic exponent z, and the central charge c. A transition at J_{c1} between the FM_{x} and FM_{z} phases is identified as a Gaussian transition with central charge c=1, involving the breaking of two Z_{2} symmetries and lying beyond the conventional Landau-Ginzburg-Wilson symmetry-breaking paradigm. The transition at J_{c2} between the FM_{x} and PM phases belongs to the quantum Ising universality class, characterized by c=1/2 and breaking of a single Z_{2} symmetry.
Building on the recently developed quantum state texture resource theory, we exhibit that the difference between maximum and minimum textures is a valid purity monotone in any dimension and provide a lower bound for existing purity measures. We introduce a texture-based resource monotone applicable across general convex resource theories, encompassing quantum coherence, non-stabilizerness, and entanglement. In particular, we propose the notion of non-local texture, which corresponds to the geometric measure of bipartite and multipartite entanglement in pure states. Furthermore, we demonstrate that the texture of the entire ground state or its subsystems can effectively signal quantum phase transitions in the Ising chain under both transverse and longitudinal magnetic fields, offering a powerful tool for characterizing quantum criticality.
Fidelity has been widely used to detect various types of quantum phase transitions (QPTs). However, challenges remain in locating the transition points with precision in several models with unconventional phases. We propose the fidelity map approach to detect QPTs with higher accuracy and sensitivity than the conventional fidelity measures. Our scheme extends the fidelity concept from a single-dimensional to a multidimensional quantity and uses a metaheuristic algorithm to search for the critical points that globally maximize the fidelity within each phase. We verify the scheme in several interacting models that possess unconventional phases and QPTs, namely, the spin-1 Kitaev-Heisenberg model, the spin-21 XXZ model, and the interacting Su-Schrieffer-Heeger model. The fidelity map can capture a wide range of phase transitions accurately even in small systems, thus providing a convenient tool to study QPTs in unseen models without prior knowledge of the symmetry of the system.