Speaker
Gerardo Ortiz
Description
In this talk I present a theoretical framework and a
computational method to study the coexistence and
competition of thermodynamic phases, and excitations, in
strongly correlated quantum Hamiltonian systems. The general
framework is known as Hierarchical Mean-Field Theory
(HMFT), and its essence revolves around the concept of the
relevant elementary degree of freedom (EDOF), e.g., a spin
cluster, utilized to build up the system. The system
Hamiltonian is then rewritten in terms of these
coarse-grained variables and a mean-field (Lie-algebraic)
approximation is performed to compute properties of the
system. Thus, the (generally) exponentially hard problem of
determining, for instance, the ground state of the system
is reduced to a polynomially complex one. At the same time,
essential quantum correlations, which drive the physics of
the problem, are captured by this local representation.
Provided the EDOF is chosen properly, even a simple single
mean-field approximation, performed on this EDOF, will yield
the correct and complete phase diagram, including its phase
transition boundaries, {\it in a single computation}. The
HMFT predictive power stems from the simple fact that a {\it
single} class of states, determined by the EDOF, is used to
establish the entire phase diagram of the system. I will
describe the zero and finite temperature formulations of the
HMFT, and illustrate the plethora of systems where the
method has been successfully applied. Examples include
frustrated spin systems with exotic magnetic phases,
including chiral ones, ring-exchange hard-core boson models,
and multiferroics.
