129 research outputs found
Valence Bond Mapping of Antiferromagnetic Spin Chains
Boson mapping techniques are developed to describe valence bond correlations
in quantum spin chains. Applying the method to the alternating bond hamiltonian
for a generic spin chain, we derive an analytic expression for the transition
points which gives perfect agreement with existing Density Matrix
Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) calculations.Comment: 10 pages, Revte
Fully Self-consistent RPA description of the many level pairing model
The Self-Consistent RPA (SCRPA) equations in the particle-particle channel
are solved without any approximation for the picket fence model. The results
are in excellent agreement with the exact solutions found with the Richardson
method. Particularly interesting features are that screening corrections
reverse the sign of the interaction and that SCRPA yields the exact energies in
the case of two levels with two particles.Comment: 37 pages, 1 figure and 17 table
Composite Boson Mapping for Lattice Boson Systems
We present a canonical mapping transforming physical boson operators into
quadratic products of cluster composite bosons that preserves matrix elements
of operators when a physical constraint is enforced. We map the 2D lattice
Bose-Hubbard Hamiltonian into composite bosons and solve it at mean
field. The resulting Mott insulator-superfluid phase diagram reproduces well
Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole
symmetry line is unraveled and in remarkable agreement with experiment. Results
for the properties of the ground and excited states are competitive with other
state-of-the-art approaches, but at a fraction of their computational cost. The
composite boson mapping here introduced can be readily applied to frustrated
many-body systems where most methodologies face significant hurdles.Comment: 8 pages, 4 figure
Commensurability effects for fermionic atoms trapped in 1D optical lattices
Fermionic atoms in two different hyperfine states confined in optical
lattices show strong commensurability effects due to the interplay between the
atomic density wave (ADW) ordering and the lattice potential. We show that
spatially separated regions of commensurable and incommensurable phases can
coexist. The commensurability between the harmonic trap and the lattice sites
can be used to control the amplitude of the atomic density waves in the central
region of the trap.Comment: Accepted for publication in Physical Review Letter
Staircase of crystal phases of hard-core bosons on the Kagome lattice
We study the quantum phase diagram of a system of hard-core bosons on the
Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary
densities, by means of the hierarchical mean field theory and exact
diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ
model in presence of an external magnetic field, a paradigmatic example of
frustrated quantum magnetism. In the non-frustrated regime, we find two crystal
phases at densities 1/3 and 2/3 that melt into a superfluid phase when
increasing the hopping amplitude, in semi-quantitative agreement with quantum
Monte Carlo computations. In the frustrated regime and away from half-filling,
we find a series of plateaux with densities commensurate with powers of 1/3.
The broader density plateaux (at densities 1/3 and 2/3) are remnants of the
classical degeneracy in the Ising limit. For densities near half-filling, this
staircase of crystal phases melts into a superfluid, which displays finite
chiral currents when computed with clusters having an odd number of sites. Both
the staircase of crystal phases and the superfluid phase prevail in the
non-interacting limit, suggesting that the lowest dispersionless
single-particle band may be at the root of this phenomenon
Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
We study the zero temperature phase diagram of two-dimensional hard-core
bosons on a square lattice with nearest neighbour and plaquette (ring-exchange)
hoppings, at arbitrary densities, by means of a hierarchical mean-field theory.
In the frustrated regime, where quantum Monte Carlo suffers from a sign
problem, we find a rich phase diagram where exotic states with nonzero
chirality emerge. Among them, novel insulating phases, characterized by nonzero
bond-chirality and plaquette order, are found over a large region of the
parameter space. In the unfrustrated regime, the hierarchical mean-field
approach improves over the standard mean-field treatment as it is able to
capture the transition from a superfluid to a valence bond state upon
increasing the strength of the ring-exchange term, in qualitative agreement
with quantum Monte Carlo results
Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian
The failures of single-reference coupled cluster for strongly correlated
many-body systems is flagged at the mean-field level by the spontaneous
breaking of one or more physical symmetries of the Hamiltonian. Restoring the
symmetry of the mean-field determinant by projection reveals that coupled
cluster fails because it factorizes high-order excitation amplitudes
incorrectly. However, symmetry-projected mean-field wave functions do not
account sufficiently for dynamic (or weak) correlation. Here we pursue a merger
of symmetry projection and coupled cluster theory, following previous work
along these lines that utilized the simple Lipkin model system as a testbed [J.
Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a
symmetry-projected mean-field wave function to the concept of a symmetry
projected state, in which the factorization of high-order excitation amplitudes
in terms of low-order ones is guided by symmetry projection and is not
exponential, and combine them with coupled cluster theory in order to model the
ground state of the Agassi Hamiltonian. This model has two separate channels of
correlation and two separate physical symmetries which are broken under strong
correlation. We show how the combination of symmetry collective states and
coupled cluster is effective in obtaining correlation energies and order
parameters of the Agassi model throughout its phase diagram
Exactly solvable Richardson–Gaudin models and their applications
3 pages, 1 table, 1 figure.--PACS nrs.: 21.60.Cs, 21.60.Fw, 02.30.Ik.--Arxiv pre-print available at: http://arxiv.org/abs/math-ph/0609022v1We first show that the quantum pairing problem can be mapped exactly on to a classical electrostatic problem in two dimensions and then use this analogy to obtain a pictorial representation of how superconductivity arises in a finite fermionic system. Specific application to the nuclei 114−116Sn suggests some new insight into the evolution of pairing
correlations in a quantum system with few active particles. We also summarize other recent work on exactly solvable pairing models, including their applications in a wide variety of strongly correlated quantum systems.The work reported herein was supported
in part by the US National Science Foundation under grant no PHY-0140036 and in part by the Spanish DGI under grant
no BFM2003-05316-C02-02.Peer reviewe
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