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arXiv:cond-mat/9304016 · Physical review. B, Condensed matter

Disordered boson systems: A perturbative study

Lizeng Zhang

Published Jun 1, 1993• 27 citations
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Abstract

A hard-core disordered boson system is mapped onto a quantum spin-1/2 XY model with transverse random fields. It is then generalized to a system of spins with an arbitrary magnitude S and studied through a 1/S expansion. The first-order 1/S expansion corresponds to a spin-wave theory. The effect of weak disorder is studied perturbatively within such a first-order 1/S scheme. We compute the reduction of the speed of sound and the lifetime of the Bloch phonons in the regime of weak disorder. Generalizations of the present study to the strong disordered regime are discussed.

DOI
10.1103/physrevb.47.14364

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A hard-core disordered boson system is mapped onto a quantum spin-1/2 XY model with transverse random fields. It is then generalized to a system of spins with an arbitrary magnitude S and studied through a 1/S expansion. The first-order 1/S expansion corresponds to a spin-wave theory. The effect of weak disorder is studied perturbatively within such a first-order 1/S scheme. We compute the reduction of the speed of sound and the lifetime of the Bloch phonons in the regime of weak disorder. Generalizations of the present study to the strong disordered regime are discussed.
We investigate the critical phenomena of hard-core bosons in a disordered medium. Such a system is mapped onto a quantum spin-1/2 XY model with transverse random field. The system then is studied through a quantum real-space renormalization-group method. We find that randomness is always relevant in a one-dimensional (1D) system, in agreement with exact results. In two and three dimensions, there is a critical amount of disorder, below which the superfluid phase is stable. In 2D, the dynamic exponent z=1.7 for compressible states, and is close to the value of z=d as predicted by Fisher et al. $z--- is smaller for incompressible states. The correlation length exponent \ensuremath{\nu} is insensitive to z, and roughly equals 1.4. Unlike the superfluid--Mott-insulator transition without disorder, which has two distinct universality classes, we find there is only one universality class for the superfluid--Bose-glass transition.
The authors consider a random magnetic model which is related to Bose condensation in the presence of a random potential. It is an XY model with a random z field. The classical model always has an ordered ground state. The nature of the ground state is unusual: the main contribution to the spontaneous magnetisation comes from a dilute set of weakly interacting pairs of spins. Within each pair the spins are strongly coupled, so for low-energy dynamics only the motion of the total spin of the pair is relevant. This allows the construction of an effective Hamiltonian only involving the pairs' total spins. When this is semi-classically quantised via a 1/S expansion, they find that the zero-point spin wave motion destroys the magnetised ground state if either the number of spin states is sufficiently small (for fixed strength of disorder), or for sufficiently large disorder (for fixed number of spin states). Finally they discuss the relation of the model to the problem of Bose condensation in a random potential, where the interaction strength is related to the number of spin states in the spin model.
This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.
We consider a generalization of the hard-core disordered boson system with the inclusion of random boson hopping. The phase diagrams are obtained, and the effects of the random boson hopping on the zero-temperature quantum phase transitions are studied. The existence of Bose-glass and superfluid glass phases is also investigated. The behavior of both continuous and first-order transitions as well as the tricritical point is discussed as a function of the strength of random on-site energies. The possible Bose glass displayed by the system due to the presence of the disorder is examined. \textcopyright{} 1996 The American Physical Society.
Disorder modifies the sound-wave excitation spectrum of Bose-Einstein condensates. We consider the classical hydrodynamic limit, where the disorder correlation length is much longer than the condensate healing length. By perturbation theory, we compute the phonon lifetime and the correction to the speed of sound. This correction is found to be negative in all dimensions, with universal asymptotics for smooth correlations. Considering in detail optical speckle potentials, we find a quite rich intermediate structure. This has consequences for the average density of states, particularly in one dimension, where we find a ``boson dip'' next to a sharp ``boson peak'' as function of frequency. In one dimension, our prediction is verified in detail by a numerical integration of the Gross-Pitaevskii equation.