• Open Access

Fidelity Susceptibility Made Simple: A Unified Quantum Monte Carlo Approach

Lei Wang, Ye-Hua Liu, Jakub Imriška, Ping Nang Ma, and Matthias Troyer
Phys. Rev. X 5, 031007 – Published 15 July 2015

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 to both the ground-state and nonzero-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.

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  • Received 10 March 2015

DOI:https://doi.org/10.1103/PhysRevX.5.031007

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Lei Wang1, Ye-Hua Liu1, Jakub Imriška1, Ping Nang Ma2, and Matthias Troyer1

  • 1Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
  • 2Yotcopi Technologies, National University of Singapore, 117576, Singapore

Popular Summary

Quantum Monte Carlo methods simulate quantum systems on a classic computer by mapping them to classical statistical mechanics problems; this step makes the simulation computationally feasible. In a broad range of modern quantum Monte Carlo methods, there exists a unifying physical picture for this corresponding classical system: interacting “particles” on a ring given by a periodic imaginary time axis whose circumference is the inverse temperature. These particles represent, for example, interaction events of the original quantum-mechanical system, and their fugacity is given by the coupling strengths of the quantum Hamiltonian.

This quantum-to-classical mapping suggests a simple yet generic approach to detecting quantum phase transitions driven by the change of the coupling strength. Instead of resorting to the details of the quantum-mechanical Hamiltonian, one can monitor a transition of the classical particles driven by the change of the fugacity. This leads to an efficient and elegant approach to calculating the fidelity susceptibility, a general-purpose indicator of quantum phase transitions from the quantum-information perspective. We have simplified the calculation of the fidelity susceptibility, and it has become easy enough to be used as a standard tool to detect quantum phase transitions.

Our results are particularly advantageous for exploring elusive and exotic phase transitions, including topological ones, where the conventional paradigm based on local order parameters is not applicable.

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Vol. 5, Iss. 3 — July - September 2015

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