Symmetry breaking in a quantum double-well chain Page: 2 of 9
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Symmetry Breaking in a Quantum I)ouble-Well Chain
J. E. Gubernatis, Theoretical Division
Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
D. K. Campbell and Xidi Wang, Center for Nonlinear Studies
Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
Abstract. We present numerical evidence that quantum fluctuations can pro-
duce a symmetric ground-state in the double-well chain, restoring the symmetry
that is broken classically. In particular, we present the phase diagram for this
model that shows the symmetry restoration occurs more easily than predicted
by a perturbation theory calculation of the continuum limit of the model.
1. Introduction
The double-well chain chain is a system of particles that move on a lattice of
symmetric, double-well potentials which are coupled harmonically to one an-
other. The phynical properties of this system are invariant to changing the sign
of the displacement variables, and this symmetry leads to a doubly-degenerate
ground-state. Classically, this symmetry is always broken, and the particles
all sit in the left- or the right-hand side of their wells. Quantum mechanically,
however, we find a range of model parameters for which symmetry is restored
by quantum fluctuations.
Our interest in this model was motivated by a series of quantum Monte
Carlo simulations we are performing on one-dimensional, electron-phonon mod-
els of conducting polymers. Several years ago, for similar models, Fradkin and
Hirsch [1] investigated how the electron motion can generate an effective double-
well potential for the phonons and thereby cause the lattice to dimerize. They
also argued that for certain models quantum fluctuations at low temperatures
restore symmetry (i.e., destroy the dimerisation). The quantum double-well
chain is a simpler problem on which to study similar issues and to test new
numerical methods.
The model, however, is also interesting on its own. It is a discretized
version of a 1 + 1 dimensional quantum 0" field theory. In the continuum
version of the model, kink/anti-kink pairs are the elementary excitations above
the ground state [2]. One of our objectives was to learn more about the nature
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Gubernatis, J. E.; Campbell, D. K. & Wang, Xidi. Symmetry breaking in a quantum double-well chain, article, January 1, 1991; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1105679/m1/2/: accessed March 29, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.