54 research outputs found
Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems
In these lecture notes, we present a pedagogical review of a number of
related {\it numerically exact} approaches to quantum many-body problems. In
particular, we focus on methods based on the exact diagonalization of the
Hamiltonian matrix and on methods extending exact diagonalization using
renormalization group ideas, i.e., Wilson's Numerical Renormalization Group
(NRG) and White's Density Matrix Renormalization Group (DMRG). These methods
are standard tools for the investigation of a variety of interacting quantum
systems, especially low-dimensional quantum lattice models. We also survey
extensions to the methods to calculate properties such as dynamical quantities
and behavior at finite temperature, and discuss generalizations of the DMRG
method to a wider variety of systems, such as classical models and quantum
chemical problems. Finally, we briefly review some recent developments for
obtaining a more general formulation of the DMRG in the context of matrix
product states as well as recent progress in calculating the time evolution of
quantum systems using the DMRG and the relationship of the foundations of the
method with quantum information theory.Comment: 51 pages; lecture notes on numerically exact methods. Pedagogical
review appearing in the proceedings of the "IX. Training Course in the
Physics of Correlated Electron Systems and High-Tc Superconductors", Vietri
sul Mare (Salerno, Italy, October 2004
Time evolution of one-dimensional Quantum Many Body Systems
The level of current understanding of the physics of time-dependent strongly
correlated quantum systems is far from complete, principally due to the lack of
effective controlled approaches. Recently, there has been progress in the
development of approaches for one-dimensional systems. We describe recent
developments in the construction of numerical schemes for general
(one-dimensional) Hamiltonians: in particular, schemes based on exact
diagonalization techniques and on the density matrix renormalization group
method (DMRG). We present preliminary results for spinless fermions with
nearest-neighbor-interaction and investigate their accuracy by comparing with
exact results.Comment: Contribution for the conference proceedings of the "IX. Training
Course in the Physics of Correlated Electron Systems and High-Tc
Superconductors" held in Vietri sul Mare (Salerno, Italy) in October 200
Time evolution of correlations in strongly interacting fermions after a quantum quench
Using the adaptive time-dependent density matrix renormalization group, we
study the time evolution of density correlations of interacting spinless
fermions on a one-dimensional lattice after a sudden change in the interaction
strength. Over a broad range of model parameters, the correlation function
exhibits a characteristic light-cone-like time evolution representative of a
ballistic transport of information. Such behavior is observed both when
quenching an insulator into the metallic region and also when quenching within
the insulating region. However, when a metallic state beyond the quantum
critical point is quenched deep into the insulating regime, no indication for
ballistic transport is observed. Instead, stable domain walls in the density
correlations emerge during the time evolution, consistent with the predictions
of the Kibble-Zurek mechanism.Comment: Published version; minor changes, references adde
Correlations and enlarged superconducting phase of - chains of ultracold molecules on optical lattices
We compute physical properties across the phase diagram of the -
chain with long-range dipolar interactions, which describe ultracold polar
molecules on optical lattices. Our results obtained by the density-matrix
renormalization group (DMRG) indicate that superconductivity is enhanced when
the Ising component of the spin-spin interaction and the charge component
are tuned to zero, and even further by the long-range dipolar interactions.
At low densities, a substantially larger spin gap is obtained. We provide
evidence that long-range interactions lead to algebraically decaying
correlation functions despite the presence of a gap. Although this has recently
been observed in other long-range interacting spin and fermion models, the
correlations in our case have the peculiar property of having a small and
continuously varying exponent. We construct simple analytic models and
arguments to understand the most salient features.Comment: published version with minor modification
Topological invariants and interacting one-dimensional fermionic systems
We study one-dimensional, interacting, gapped fermionic systems described by
variants of the Peierls-Hubbard model and characterize their phases via a
topological invariant constructed out of their Green's functions. We
demonstrate that the existence of topologically protected, zero-energy states
at the boundaries of these systems can be tied to the values of their
topological invariant, just like when working with the conventional,
noninteracting topological insulators. We use a combination of analytical
methods and the numerical density matrix renormalization group method to
calculate the values of the topological invariant throughout the phase diagrams
of these systems, thus deducing when topologically protected boundary states
are present. We are also able to study topological states in spin systems
because, deep in the Mott insulating regime, these fermionic systems reduce to
spin chains. In this way, we associate the zero-energy states at the end of an
antiferromagnetic spin-one Heisenberg chain with the topological invariant 2.Comment: 15 pages, 11 figures, Final Version as published in PR
Finite-Temperature Dynamics and Thermal Intraband Magnon Scattering in Haldane Spin-One Chains
The antiferromagnetic spin-one chain is considerably one of the most
fundamental quantum many-body systems, with symmetry protected topological
order in the ground state. Here, we present results for its dynamical spin
structure factor at finite temperatures, based on a combination of exact
numerical diagonalization, matrix-product-state calculations and quantum Monte
Carlo simulations. Open finite chains exhibit a sub-gap band in the thermal
spectral functions, indicative of localized edge-states. Moreover, we observe
the thermal activation of a distinct low-energy continuum contribution to the
spin spectral function with an enhanced spectral weight at low momenta and its
upper threshold. This emerging thermal spectral feature of the Haldane spin-one
chain is shown to result from intra-band magnon scattering due to the thermal
population of the single-magnon branch, which features a large bandwidth-to-gap
ratio. These findings are discussed with respect to possible future studies on
spin-one chain compounds based on inelastic neutron scattering.Comment: 10 pages with 11 figures total (including Supplemental Material);
changes in v2: new Figs. S1 and S5, Fig. S3 expanded + related discussion +
many smaller modifications to match published versio
Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the kagome system ZnCu_3(OH)_6Cl_2
Motivated by recent nuclear magnetic resonance experiments on
ZnCu(OH)Cl, we present an exact-diagonalization study of the
combined effects of non-magnetic impurities and Dzyaloshinskii-Moriya (DM)
interactions in the kagome antiferromagnet. The local response to an
applied field and correlation-matrix data reveal that the dimer freezing which
occurs around each impurity for persists at least up to , where and denote respectively the exchange and DM interaction
energies. The phase transition to the () semiclassical, 120
state favored at large takes place at . However, the dimers
next to the impurity sites remain strong up to values , far above
this critical point, and thus do not participate fully in the ordered state. We
discuss the implications of our results for experiments on
ZnCu(OH)Cl.Comment: 11 pages, submitted to PR
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