Hierarchical Mean-Field Theories in Quantum Statistical Mechanics

Abstract

We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian, modeling the system, can always be written in a hierarchical operator language that unveils all symmetry generators of the problem and, thus, possible thermodynamic phases. In general one cannot compute the thermodynamic or zero-temperature properties exactly and an approximate scheme named ``hierarchical mean-field approach'' is introduced. This approach treats all possible competing orders on an equal footing. We illustrate the methodology by determining the phase diagram and quantum critical point of a bosonic lattice model which displays coexistence and competition between antiferromagnetism and superfluidity.

4 pages, 2 psfigures. submitted Phys. Rev. B

References in corpus (2)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation

Cited by in corpus (7)

• Generalizations of entanglement based on coherent states and convex sets
• Algebraic Approach to Interacting Quantum Systems
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Equivalence of Topological Insulators and Superconductors
• Phase diagram of the Heisenberg antiferromagnet with four-spin interactions
• Emergent magnetic order in the antiferromagnetic Kitaev model with a [111] field