- 93-292 Tohru Koma, Hal Tasaki
- Obscured Symmetry Breaking and Low-Lying Excited States
Nov 11, 93
(auto. generated ps),
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Abstract. We consider a quantum many-body system
on a lattice which exhibits a
spontaneous symmetry breaking in its infinite volume ground states,
but in which
the corresponding order operator does not commute with the
In the corresponding finite system, the symmetry breaking is usually
``obscured'' by ``quantum fluctuation''
and one gets a symmetric ground
state with a long range order.
In such a situation, Horsch and von der Linden proved
that the finite system has a low-lying
whose energy per site converges to the ground state energy per site
as the system size increases.
When the system has a continuous symmetry, we prove that the
number of independent low-lying eigenstates grows faster than
any given small
of the system size.
We show that a translation invariant low-lying state converges
to a ground state in the infinite volume limit.
We also construct infinite
volume ground states with explicit symmetry breaking by taking
linear combinations of the (finite-volume) ground state and
the low-lying states, and then taking infinite volume limits.
We conjecture these infinite volume ground states
to be pure.
Our general theorems do not only shed light on the nature of
symmetry breaking in quantum many-body systems, but
provide indispensable information for numerical approaches
to these systems.
We also discuss applications of our general results to a
variety of interesting examples.