12,430 research outputs found
Hidden unity in the quantum description of matter
We introduce an algebraic framework for interacting quantum systems that
enables studying complex phenomena, characterized by the coexistence and
competition of various broken symmetry states of matter. The approach unveils
the hidden unity behind seemingly unrelated physical phenomena, thus
establishing exact connections between them. This leads to the fundamental
concept of {\it universality} of physical phenomena, a general concept not
restricted to the domain of critical behavior. Key to our framework is the
concept of {\it languages} and the construction of {\it dictionaries} relating
them.Comment: 10 pages 2 psfigures. Appeared in Recent Progress in Many-Body
Theorie
Hierarchical Mean-Field Theories in Quantum Statistical Mechanics
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.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.
Stripes, topological order, and deconfinement in a planar t-Jz model
We determine the quantum phase diagram of a two-dimensional bosonic t-Jz
model as a function of the lattice anisotropy gamma, using a quantum Monte
Carlo loop algorithm. We show analytically that the low-energy sectors of the
bosonic and the fermionic t-Jz models become equivalent in the limit of small
gamma. In this limit, the ground state represents a static stripe phase
characterized by a non-zero value of a topological order parameter. This phase
remains up to intermediate values of gamma, where there is a quantum phase
transition to a phase-segregated state or a homogeneous superfluid with dynamic
stripe fluctuations depending on the ratio Jz/t.Comment: 4 pages, 5 figures (2 in color). Final versio
- …