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arXiv:cond-mat/9612208 · Journal of Physics A Mathematical and General

Quantum Monte Carlo simulations of a particle in a random potential

Hsuan‐Yi Chen, Yadin Y. Goldschmidt

Published Mar 21, 1997• 3 citations
arXivHTMLPDF

Abstract

In this paper we carry out quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample-to-sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behaviour is discussed.

DOI
10.1088/0305-4470/30/6/008

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In this paper we carry out quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample-to-sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behaviour is discussed.
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.
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.
We study the zero-temperature behaviour of the infinite-ranged Ising spin glass in a transverse field. Using spin summation and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value for the correlation length exponent, z=4 for the dynamical exponent and an algebraic decay for the imaginary-time correlation function. The zero-temperature Monte Carlo relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground-state energy due to quantum fluctuations and displays glassy effects due to the strong anisotropy in the effective Hamiltonian.
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered – glassy – phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random king chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.
We study the effect of diagonal disorder on a one-dimensional (1-D) Hubbard model by means of a Monte Carlo simulation. Contrary to previous analytical studies of interacting disordered systems in one dimension, the numerical simulation is not restricted to the weak coupling regime in disorder and/or interaction. Quantum fluctuations are introduced using the scheme developed by J. Hirsch [Phys. Rev. B 31, 4403 (1985)] for Grand Canonical ensembles and arbitrary dimensions. A second Monte Carlo loop creates the configurations for the disorder potential. Preliminary results for various correlation functions are presented.
Abstract We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the intensity of the transverse field. We use a combination of quantum Monte Carlo algorithms and exact diagonalization to compute Rényi entropies, quantum Fisher information, correlation functions and order parameter. We locate the transition by means of the peak of the Rényi entropy and we find agreement with the transition point estimated from the emergence of finite values of the Edwards–Anderson order parameter and from the peak of the correlation length. We interpret the results by means of a mean-field theory in which quantum fluctuations are treated as massive particles hopping on the interaction graph. We see that the particles are delocalized at the transition, a fact that points towards the existence of possibly another transition deep in the glassy phase where these particles localize, therefore leading to a many-body localized phase.