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arXiv:0907.0191 · Physical Review Letters

Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions

David R. Schwandt, Fabien Alet, Sylvain Capponi

Published Oct 19, 2009• 134 citations
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Abstract

When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.

DOI
10.1103/physrevlett.103.170501

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When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
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The deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken-symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly-first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study the deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density-matrix renormalization-group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the idea that the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size-scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at the deconfined quantum critical point from the concept of quantum information.
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