Fidelity susceptibility made simple: A unified quantum Monte Carlo approach

Abstract

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied both to the ground-state and non-zero temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-$1/2$ XXZ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.

new physical insight added in Sec. VI., improved data in Fig. 6

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• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Entanglement Entropy and Complexity for One-Dimensional Holographic Superconductors
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Fidelity Susceptibility in the Quantum Rabi Model
• Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Detecting phase transitions and crossovers in Hubbard models using the fidelity susceptibility
• Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Spin-singlet and spin-triplet pairing correlations in antiferromagnetically coupled Kondo systems
• Adiabatic Sensing Enhanced by Quantum Criticality