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Progress of Theoretical Physics Supplement

Static and Dynamic Holes in a Quantum Critical Antiferromagnet

Matthias Troyer

Published Jan 1, 2002• 18 citations
Publisher

Abstract

I compute the properties of a mobile hole or a static impurity injected into a quantum critical two-dimensional antiferromagnet by quantum Monte Carlo simulations. Using field-theoretical results by Sachdev et al. the mobile hole problem is mapped to the static impurity one and can thus also be treated in quantum Monte Carlo simulations without a negative sign problem.

DOI
10.1143/ptps.145.326

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I compute the properties of a mobile hole or a static impurity injected into a quantum critical two-dimensional antiferromagnet by quantum Monte Carlo simulations. Using field-theoretical results by Sachdev et al. the mobile hole problem is mapped to the static impurity one and can thus also be treated in quantum Monte Carlo simulations without a negative sign problem.
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A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.
Using the standard quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a quantum antiferromagnet. The calculation is very well stabilized, using selected-size systems and a special choice of the trial wave function that satisfies the ``closed-shell condition'' in the presence of an arbitrarily weak Zeeman magnetic field. First it is shown that the presence of this magnetic field does not affect the thermodynamic properties of the half-filled system. Then I use the same selected sizes for the one-hole ground state. I investigate the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator behaves as a conventional insulator with an upper and lower Hubbard band. By comparing the present finite-size scaling with several techniques that predict a finite quasiparticle weight, the data seem more consistent with a vanishing quasiparticle weight, i.e., the Mott-Hubbard insulator should be characterized by nontrivial excitations that cannot be interpreted in a simple picture. However, one cannot exclude, based only on numerical grounds, a very small but nonvanishing quasiparticle weight. In the last part I give some theoretical arguments to explain the results of the Monte Carlo simulation.