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ABSTRACT: Current widely-used approaches to calculate spectral functions using the
density-matrix renormalization group in frequency space either necessarily
include an artificial broadening (correction-vector method) or have limited
resolution (time-domain density-matrix renormalization group with Fourier
transform method). Here we propose an adaptive Lanczos-vector method to
calculate the coefficients of a continued fraction expansion of the spectral
function iteratively. We show that one can obtain a very accurate
representation of the spectral function very efficiently, and that one can also
directly extract the spectral weights and poles for the discrete system. As a
test case, we study spinless fermions in one dimension and compare our approach
to the correction vector method.
Physical Review B 04/2011; 83(16):161104(R). · 3.69 Impact Factor
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ABSTRACT: Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.
Physical Review Letters 06/2007; 98(21):210405. · 7.37 Impact Factor
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A. F. Albuquerque,
F. Alet,
P. Corboz,
P. Dayal,
A. Feiguin,
S. Fuchs,
L. Gamper,
E. Gull,
S. Guertler,
A. Honecker, [......], R. M. Noack,
G. Pawlowski,
L. Pollet,
T. Pruschke,
U. Schollwock,
S Todo,
S. Trebst,
M. Troyer,
P Werner,
S. Wessel
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ABSTRACT: We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/ .
Journal of Magnetism and Magnetic Materials 03/2007; 310(2):1187–1193. · 1.78 Impact Factor
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A.F. Albuquerque,
F. Alet,
P. Corboz,
P. Dayal,
A. Feiguin,
S. Fuchs,
L. Gamper,
E. Gull,
S. Gürtler,
A. Honecker, [......], R.M. Noack,
G. Pawłowski,
L. Pollet,
T. Pruschke,
U. Schollwöck,
S. Todo,
S. Trebst,
M. Troyer,
P. Werner,
S. Wessel
[show abstract]
[hide abstract]
ABSTRACT: We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open-source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/.
Journal of Magnetism and Magnetic Materials 03/2007; 310(2):1187-1193. · 1.78 Impact Factor
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ABSTRACT: We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin 1/2 dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the ${\bf D}$ vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes {\it perpendicular} to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35 g\mu_B$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of inter-dimer coupling in the context of ladders with Density Matrix Renormalization Group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on Cu$_{2}$(C$_{5}$H$_{12}$N$_{2}$)$_{2}$Cl$_{4}$. Comment: 8 pages, 9 figures
10/2006;
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ABSTRACT: We study the formation of (quasi-)coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi-condensate emerges at momentum k=\pi/2a, where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan-Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.
07/2006;
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ABSTRACT: Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaux. In particular, anisotropic interactions generically open a gap in the region between the plateaux, but we show that this gap closes upon entering fractional plateaux. All of these conclusions, based on analytical arguments, are supported by extensive Density Matrix Renormalization Group calculations.
04/2006;
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ABSTRACT: Motivated by the recent discovery of the spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in the gapped phase and slightly beyond. The implications for [(CuCl$_2$tachH)$_3$Cl]Cl$_2$ are discussed, with the conclusion that this system behaves essentially as a spin-3/2 chain.
10/2005;
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F. Alet,
P. Dayal,
A. Grzesik,
A. Honecker,
M. Koerner,
A. Laeuchli,
S. R. Manmana,
I. P. McCulloch,
F. Michel, R. M. Noack,
G. Schmid,
U. Schollwoeck,
F. Stoeckli,
S. Todo,
S. Trebst,
M. Troyer,
P. Werner,
S. Wessel,
for the ALPS collaboration
[show abstract]
[hide abstract]
ABSTRACT: We present the ALPS (Algorithms and Libraries for Physics Simulations)
project, an international open source software project to develop libraries and
application programs for the simulation of strongly correlated quantum lattice
models such as quantum magnets, lattice bosons, and strongly correlated fermion
systems. Development is centered on common XML and binary data formats, on
libraries to simplify and speed up code development, and on full-featured
simulation programs. The programs enable non-experts to start carrying out
numerical simulations by providing basic implementations of the important
algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC)
using non-local updates, extended ensemble simulations, exact and full
diagonalization (ED), as well as the density matrix renormalization group
(DMRG). The software is available from our web server at
http://alps.comp-phys.org.
Journal of the Physical Society of Japan Supplement. 01/2005; 74:30.
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ABSTRACT: We study the zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give strong evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong coupling phase can only partly be understood in terms of the strong coupling behavior of the ordinary Hubbard model. Comment: 18 pages, 16 figures, submitted to Phys. Rev. B
07/2003;
