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arXiv:cond-mat/9607044 · Physical review. B, Condensed matter

Quantum critical effects in mean-field glassy systems

Félix Ritort

Published Jun 1, 1997• 12 citations
arXivHTMLPDF

Abstract

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

DOI
10.1103/physrevb.55.14096

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We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.
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In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ``toy'' model for an interface in a random medium. It also applies to a single quantum particle such as an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use of the replica method, we are able to solve the model and obtain its phase diagram in the T-(${\mathrm{\ensuremath{\Elzxh}}}^{2}$/m) plane, where m is the particle's mass. The phase diagram is similar to that of a quantum spin glass in a transverse field, where the variable ${\mathrm{\ensuremath{\Elzxh}}}^{2}$/m plays the role of the transverse field. The glassy phase is characterized by replica symmetry breaking. The quantum transition at zero temperature is also discussed. \textcopyright{} 1996 The American Physical Society.
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We study effects of random fluctuations in quantum spin-glass systems. We show that the expression of the magnetic susceptibility is divided into the classical and quantum parts. The former can be analyzed by the standard replica method with the static approximation. The latter incorporates dynamical correlations and is determined by the energy gap distribution. By using the many-body interacting Ising spin-glass model with transverse field, we discuss possible mechanisms of the quantum phase transitions.
A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$,TTT plane is also given.