Fidelity susceptibility probes of dynamical quantum criticality

Amit Dutta

Yukun Zhang, Xiao Yuan

The fidelity susceptibility serves as a universal probe for quantum phase transitions, offering an order-parameter-free metric that captures ground-state sensitivity to Hamiltonian perturbations and exhibits critical scaling. Classical computation of this quantity, however, is limited by exponential Hilbert space growth and correlation divergence near criticality, restricting analyses to small or specialized systems. Here, we present a quantum algorithm that achieves efficient and Heisenberg-limited estimation of fidelity susceptibility through a novel resolvent reformulation and pseudoinverse block encoding leveraging quantum singular value transformation and amplitude estimation for norm evaluation. This constitutes the first quantum algorithm for fidelity susceptibility with optimal precision scaling. Moreover, for frustration-free Hamiltonians, we show that the resolvent can be approximated with a further quadratic speedup. Beyond fidelity susceptibility, our resolvent-based framework applies broadly to observables expressible through spectral sums or linear response functions, suggesting a systematic approach to quantum algorithm design for many-body physics. Our Letter bridges quantum many-body physics and algorithmic design, enabling scalable exploration of quantum criticality with applications in materials simulation and metrology on fault-tolerant quantum platforms.

Yu-Bin Liu, Wen-Yi Zhang, Tian-Cheng Yi +3 more

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

Shi-Jian Gu

Wing Chi Yu, Ho-Man Kwok, Junpeng Cao +1 more

Changjing Zeng, Zhen Cai, Guang-Heng Wang +1 more

Abstract We study the critical behaviors of the ground and first-excited states in the one-dimensional nonreciprocal Aubry-André-Harper (AAH) model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as N 2 , akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as N 2 . In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law.