arXiv subjects

U. Schollwöck

Publications and source records attributed to U. Schollwöck.

At least 19 recordsLinked to original sources

arXiv2023

Complex Time Evolution in Tensor Networks

Real-time calculations in tensor networks are strongly limited in time by entanglement growth, restricting the achievable frequency resolution of Green's functions, spectral functions, self-energies, and other related quantities. By extending the time evolution to contours in the complex plane, entanglement growth is curtailed, enabling numerically efficient high-precision calculations of time-dependent correlators and Green's functions with detailed frequency resolution. Various approaches to time evolution in the complex plane and the required post-processing for extracting the pure real-time and frequency information are compared. We benchmark our results on the examples of the single-impurity Anderson model using matrix-product states and of the three-band Hubbard-Kanamori and Dworin-Narath models using a tree tensor network. Our findings indicate that the proposed methods are also applicable to challenging realistic calculations of materials.

cond-mat.str-el↗

arXiv2020

Thermal control of spin excitations in the coupled Ising-chain material RbCoCl3

We have used neutron spectroscopy to investigate the spin dynamics of the quantum (S = 1/2) antiferromagnetic Ising chains in RbCoCl3. The structure and magnetic interactions in this material conspire to produce two magnetic phase transitions at low temperatures, presenting an ideal opportunity for thermal control of the chain environment. The high-resolution spectra we measure of two-domain-wall excitations therefore characterize precisely both the continuum response of isolated chains and the "Zeeman-ladder" bound states of chains in three different effective staggered fields in one and the same material. We apply an extended Matsubara formalism to obtain a quantitative description of the entire dataset, Monte Carlo simulations to interpret the magnetic order, and finite-temperature DMRG calculations to fit the spectral features of all three phases.

cond-mat.str-el↗

arXiv2019

Dynamical topological quantum phase transitions in nonintegrable models

We consider sudden quenches across quantum phase transitions in the $S=1$ XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.

cond-mat.stat-mech↗

arXiv2019

Interaction quench and thermalization in a one-dimensional topological Kondo insulator

We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a $p$-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench influences the topological properties of the system, therefore our main focus is the time evolution of the string order parameter, entanglement spectrum and the topologically-protected edge states. We point out that postquench local observables can be well captured by a thermal ensemble up to a certain interaction strength. Our results demonstrate that the topological properties after the interaction quench are preserved. Though the absolute value of the string order parameter decays in time, the analysis of the entanglement spectrum, Loschmidt echo and the edge states indicates the robustness of the topological properties in the time-evolved state. These predictions could be directly tested in state-of-the-art cold-atom experiments.

cond-mat.str-el↗

arXiv2018

Error estimates for extrapolations with matrix-product states

We introduce a new error measure for matrix-product states without requiring the relatively costly two-site density matrix renormalization group (2DMRG). This error measure is based on an approximation of the full variance $\langle ψ| ( \hat H - E )^2 |ψ\rangle$. When applied to a series of matrix-product states at different bond dimensions obtained from a single-site density matrix renormalization group (1DMRG) calculation, it allows for the extrapolation of observables towards the zero-error case representing the exact ground state of the system. The calculation of the error measure is split into a sequential part of cost equivalent to two calculations of $\langle ψ| \hat H | ψ\rangle$ and a trivially parallelized part scaling like a single operator application in 2DMRG. The reliability of the new error measure is demonstrated at four examples: the $L=30, S=\frac{1}{2}$ Heisenberg chain, the $L=50$ Hubbard chain, an electronic model with long-range Coulomb-like interactions and the Hubbard model on a cylinder of size $10 \times 4$. Extrapolation in the new error measure is shown to be on-par with extrapolation in the 2DMRG truncation error or the full variance $\langle ψ| ( \hat H - E )^2 |ψ\rangle$ at a fraction of the computational effort.

cond-mat.str-el↗

arXiv2017

Generic Construction of Efficient Matrix Product Operators

Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.

cond-mat.str-el↗

arXiv2016

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex-fluids, vortex-lattices, charge-density-waves and the biased-ladder phase. Our work focuses on the subset of these states that break a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux-quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact to recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

cond-mat.quant-gas↗

arXiv2016

Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: Swimming against the tide

The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While non-interacting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.

cond-mat.quant-gas↗

arXiv2013

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

In magnetically ordered systems the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite size energy spectra, the so called tower of states (TOS). In the present work we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground state entanglement spectrum (ES). Using state-of-the-art DMRG calculations, we examine the ES of the 2D antiferromagnetic J1-J2 Heisenberg model on both the triangular and kagomé lattice. At large ferromagnetic J2 the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite size scaling in the thermodynamic limit) sharply reflects tower of states features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG.

cond-mat.str-el↗

arXiv2013

Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain

The space- and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behaviour. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in wavevector and energy with great detail, allowing theories to be quantitatively tested to high accuracy. Here, we present a comparison between neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on integrability and density matrix renormalization group simulations. The unprecedented quantitative agreement shows that precise descriptions of strongly correlated states at all distance, time and temperature scales are now possible, and highlights the need to apply these novel techniques to other problems in low-dimensional magnetism.

cond-mat.str-el↗

arXiv2012

Lanczos algorithm with Matrix Product States for dynamical correlation functions

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex-post reorthogonalization method allows to avoid several shortcomings of the original approach, namely the multi-targeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.

cond-mat.str-el↗

arXiv2012

Dipolar Dynamics for Interacting Ultracold Fermions in a Trapped Optical Lattice

Using the time-dependent density matrix renormalization group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.

cond-mat.quant-gas↗

arXiv2012

Dimer, trimer and FFLO liquids in mass- and spin-imbalanced trapped binary mixtures in one dimension

We present a systematic investigation of attractive binary mixtures in presence of both spin- and mass-imbalance in one dimensional setups described by the Hubbard model. After discussing typical cold atomic experimental realizations and the relation between microscopic and effective parameters, we study several many-body features of trapped Fermi-Fermi and Bose-Bose mixtures such as density profiles, momentum distributions and correlation functions by means of numerical density-matrix-renormalization-group and Quantum Monte Carlo simulations. In particular, we focus on the stability of Fulde-Ferrell-Larkin-Ovchinnikov, dimer and trimer fluids in inhomogeneous situations, as typically realized in cold gas experiments due to the harmonic confinement. We finally consider possible experimental signatures of these phases both in the presence of a finite polarization and of a finite temperature.

cond-mat.quant-gas↗

arXiv2012

Confinement: a real-time visualization

Due to the mechanism of confinement, as known from quantum chromodynamics, it is difficult to observe individual particles carrying fractional quantum number (e.g. quark with fractional electric charge). A condensed matter example of fractionalized particles is spinons in quasi-one-dimensional spin systems, which are domain walls in the background of Neel configurations carrying spin-1/2. Using the time-evolving block decimation algorithm, we visualize the nontrivial domain wall dynamics induced by the confine mechanism in a two-leg spin-1/2 ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the domain wall dynamics in the ultra-cold boson systems of $^{87}$Rb.

cond-mat.str-el↗

arXiv2011

Trapped Ultracold Bosons in Periodically Modulated Lattices

Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density-matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.

cond-mat.quant-gas↗

arXiv2011

The ALPS project release 2.0: Open source software for strongly correlated systems

We present release 2.0 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an 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. The code development is centered on common XML and HDF5 data formats, libraries to simplify and speed up code development, common evaluation and plotting tools, and simulation programs. The programs enable non-experts to start carrying out serial or parallel 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), the density matrix renormalization group (DMRG) both in a static version and a dynamic time-evolving block decimation (TEBD) code, and quantum Monte Carlo solvers for dynamical mean field theory (DMFT). The ALPS libraries provide a powerful framework for programers to develop their own applications, which, for instance, greatly simplify the steps of porting a serial code onto a parallel, distributed memory machine. Major changes in release 2.0 include the use of HDF5 for binary data, evaluation tools in Python, support for the Windows operating system, the use of CMake as build system and binary installation packages for Mac OS X and Windows, and integration with the VisTrails workflow provenance tool. The software is available from our web server at http://alps.comp-phys.org/.

cond-mat.str-el↗

arXiv2011

Quantum Spinon Oscillations

The full quantum dynamics of a spinon under external magnetic fields is investigated by using the time-evolving block decimation (TEBD) method within the microcanonical picture of transport. We show that the center of the spinon oscillates back and forth in the absence of dissipation. The quantum many-body behavior can be understood in a single-particle picture of transport and Bloch oscillations, where quantum fluctuations induce finite life times. Transport, oscillations and lifetimes can be tuned to some degree separately by external fields. Other nontrivial dynamics such as resonance as well as chaos have also been discussed.

cond-mat.str-el↗

arXiv2008

Quasiparticles in the Kondo lattice model at partial fillings of the conduction band

We study the spectral properties of the one-dimensional Kondo lattice model as function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phase. Using the density-matrix renormalization group method, we compute the dispersion relation of the quasiparticles, their lifetimes, and the Z-factor. As a main result, we provide evidence for the existence of the spinpolaron at partial band fillings. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phase and depends strongly on the quasimomentum.

cond-mat.str-el↗