September 15, 2014 to October 10, 2014
Nordita, Stockholm
Europe/Stockholm timezone

Hierarchical Mean-Field Theory

Not scheduled
132:028 (Nordita, Stockholm)


Nordita, Stockholm


Gerardo Ortiz


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.

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